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Publisher: Springer-Verlag   (Total: 2345 journals)

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Showing 1 - 200 of 2345 Journals sorted alphabetically
3D Research     Hybrid Journal   (Followers: 19, SJR: 0.214, h-index: 10)
4OR: A Quarterly J. of Operations Research     Hybrid Journal   (Followers: 9, SJR: 1.073, h-index: 25)
AAPS J.     Hybrid Journal   (Followers: 20, SJR: 1.192, h-index: 74)
AAPS PharmSciTech     Hybrid Journal   (Followers: 6, SJR: 0.718, h-index: 54)
Abdominal Imaging     Hybrid Journal   (Followers: 14, SJR: 0.723, h-index: 60)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2, SJR: 0.447, h-index: 12)
Academic Psychiatry     Full-text available via subscription   (Followers: 22, SJR: 0.492, h-index: 32)
Academic Questions     Hybrid Journal   (Followers: 7, SJR: 0.135, h-index: 6)
Accreditation and Quality Assurance: J. for Quality, Comparability and Reliability in Chemical Measurement     Hybrid Journal   (Followers: 26, SJR: 0.378, h-index: 30)
Acoustical Physics     Hybrid Journal   (Followers: 10, SJR: 0.355, h-index: 20)
Acoustics Australia     Hybrid Journal  
Acta Analytica     Hybrid Journal   (Followers: 7, SJR: 0.387, h-index: 6)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1, SJR: 0.624, h-index: 34)
Acta Biotheoretica     Hybrid Journal   (Followers: 5, SJR: 0.419, h-index: 25)
Acta Diabetologica     Hybrid Journal   (Followers: 14, SJR: 1.318, h-index: 46)
Acta Endoscopica     Hybrid Journal   (Followers: 1, SJR: 0.113, h-index: 8)
acta ethologica     Hybrid Journal   (Followers: 4, SJR: 0.465, h-index: 23)
Acta Geochimica     Hybrid Journal   (Followers: 3)
Acta Geodaetica et Geophysica     Hybrid Journal   (Followers: 1, SJR: 0.294, h-index: 13)
Acta Geotechnica     Hybrid Journal   (Followers: 7, SJR: 1.818, h-index: 22)
Acta Informatica     Hybrid Journal   (Followers: 5, SJR: 0.524, h-index: 32)
Acta Mathematica     Hybrid Journal   (Followers: 11, SJR: 8.021, h-index: 47)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2, SJR: 0.53, h-index: 29)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5, SJR: 0.406, h-index: 30)
Acta Mathematica Vietnamica     Hybrid Journal   (SJR: 0.451, h-index: 5)
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal   (SJR: 0.22, h-index: 20)
Acta Mechanica     Hybrid Journal   (Followers: 19, SJR: 0.898, h-index: 52)
Acta Mechanica Sinica     Hybrid Journal   (Followers: 5, SJR: 0.426, h-index: 29)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 5, SJR: 0.525, h-index: 18)
Acta Meteorologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.524, h-index: 14)
Acta Neurochirurgica     Hybrid Journal   (Followers: 6, SJR: 0.833, h-index: 73)
Acta Neurologica Belgica     Hybrid Journal   (SJR: 0.348, h-index: 27)
Acta Neuropathologica     Hybrid Journal   (Followers: 3, SJR: 6.61, h-index: 117)
Acta Oceanologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.295, h-index: 17)
Acta Parasitologica     Hybrid Journal   (Followers: 9, SJR: 0.581, h-index: 28)
Acta Physiologiae Plantarum     Hybrid Journal   (Followers: 2, SJR: 0.551, h-index: 39)
Acta Politica     Hybrid Journal   (Followers: 13, SJR: 0.658, h-index: 20)
adhäsion KLEBEN & DICHTEN     Hybrid Journal   (Followers: 5, SJR: 0.103, h-index: 4)
ADHD Attention Deficit and Hyperactivity Disorders     Hybrid Journal   (Followers: 20, SJR: 0.871, h-index: 15)
Adhesion Adhesives & Sealants     Hybrid Journal   (Followers: 7)
Administration and Policy in Mental Health and Mental Health Services Research     Partially Free   (Followers: 15, SJR: 0.795, h-index: 40)
Adsorption     Hybrid Journal   (Followers: 4, SJR: 0.774, h-index: 52)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3, SJR: 0.319, h-index: 15)
Advances in Atmospheric Sciences     Hybrid Journal   (Followers: 34, SJR: 0.959, h-index: 44)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15, SJR: 1.255, h-index: 44)
Advances in Contraception     Hybrid Journal   (Followers: 2)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 53, SJR: 1.113, h-index: 14)
Advances in Gerontology     Partially Free   (Followers: 9, SJR: 0.141, h-index: 3)
Advances in Health Sciences Education     Hybrid Journal   (Followers: 23, SJR: 1.397, h-index: 42)
Advances in Manufacturing     Hybrid Journal   (Followers: 3, SJR: 0.2, h-index: 4)
Advances in Polymer Science     Hybrid Journal   (Followers: 40, SJR: 0.637, h-index: 89)
Advances in Therapy     Hybrid Journal   (Followers: 5, SJR: 0.79, h-index: 44)
Aegean Review of the Law of the Sea and Maritime Law     Hybrid Journal   (Followers: 7)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2, SJR: 0.882, h-index: 23)
Aerobiologia     Hybrid Journal   (Followers: 1, SJR: 0.511, h-index: 36)
Aesthetic Plastic Surgery     Hybrid Journal   (Followers: 9, SJR: 0.821, h-index: 49)
African Archaeological Review     Hybrid Journal   (Followers: 14, SJR: 0.612, h-index: 24)
Afrika Matematika     Hybrid Journal   (Followers: 1, SJR: 0.248, h-index: 6)
AGE     Hybrid Journal   (Followers: 7, SJR: 1.358, h-index: 33)
Ageing Intl.     Hybrid Journal   (Followers: 7, SJR: 0.337, h-index: 10)
Aggiornamenti CIO     Hybrid Journal   (Followers: 1)
Aging Clinical and Experimental Research     Hybrid Journal   (Followers: 3, SJR: 0.529, h-index: 55)
Agricultural Research     Hybrid Journal   (Followers: 3)
Agriculture and Human Values     Hybrid Journal   (Followers: 12, SJR: 1.197, h-index: 49)
Agroforestry Systems     Hybrid Journal   (Followers: 19, SJR: 0.64, h-index: 56)
Agronomy for Sustainable Development     Hybrid Journal   (Followers: 10, SJR: 1.732, h-index: 59)
AI & Society     Hybrid Journal   (Followers: 6, SJR: 0.171, h-index: 19)
AIDS and Behavior     Hybrid Journal   (Followers: 13, SJR: 2.006, h-index: 71)
Air Quality, Atmosphere & Health     Hybrid Journal   (Followers: 3, SJR: 0.706, h-index: 19)
Akupunktur & Aurikulomedizin     Full-text available via subscription   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3, SJR: 0.566, h-index: 18)
Algebra Universalis     Hybrid Journal   (Followers: 2, SJR: 0.388, h-index: 22)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1, SJR: 0.868, h-index: 20)
Algorithmica     Hybrid Journal   (Followers: 7, SJR: 0.898, h-index: 56)
Allergo J.     Full-text available via subscription   (Followers: 1, SJR: 0.183, h-index: 20)
Allergo J. Intl.     Hybrid Journal   (Followers: 2)
Alpine Botany     Hybrid Journal   (Followers: 4, SJR: 0.729, h-index: 20)
ALTEX : Alternatives to Animal Experimentation     Open Access   (Followers: 3, SJR: 1.392, h-index: 32)
AMBIO     Hybrid Journal   (Followers: 14, SJR: 1.094, h-index: 87)
American J. of Cardiovascular Drugs     Hybrid Journal   (Followers: 10, SJR: 0.864, h-index: 39)
American J. of Community Psychology     Hybrid Journal   (Followers: 24, SJR: 1.237, h-index: 83)
American J. of Criminal Justice     Hybrid Journal   (Followers: 7, SJR: 0.634, h-index: 13)
American J. of Cultural Sociology     Hybrid Journal   (Followers: 11, SJR: 0.283, h-index: 3)
American J. of Dance Therapy     Hybrid Journal   (Followers: 4, SJR: 0.175, h-index: 13)
American J. of Potato Research     Hybrid Journal   (Followers: 2, SJR: 0.558, h-index: 35)
American J. of Psychoanalysis     Hybrid Journal   (Followers: 21, SJR: 0.293, h-index: 13)
American Sociologist     Hybrid Journal   (Followers: 12, SJR: 0.18, h-index: 13)
Amino Acids     Hybrid Journal   (Followers: 7, SJR: 1.362, h-index: 83)
AMS Review     Partially Free   (Followers: 4)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 5, SJR: 0.21, h-index: 37)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4, SJR: 0.665, h-index: 7)
Analysis in Theory and Applications     Hybrid Journal  
Analysis of Verbal Behavior     Hybrid Journal   (Followers: 4)
Analytical and Bioanalytical Chemistry     Hybrid Journal   (Followers: 28, SJR: 1.096, h-index: 123)
Anatomical Science Intl.     Hybrid Journal   (Followers: 2, SJR: 0.301, h-index: 26)
Angewandte Schmerztherapie und Palliativmedizin     Hybrid Journal  
Angiogenesis     Hybrid Journal   (Followers: 3, SJR: 2.212, h-index: 69)
Animal Cognition     Hybrid Journal   (Followers: 16, SJR: 1.122, h-index: 55)
Annales françaises de médecine d'urgence     Hybrid Journal   (Followers: 1, SJR: 0.156, h-index: 4)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3, SJR: 1.377, h-index: 32)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annali dell'Universita di Ferrara     Hybrid Journal   (SJR: 0.504, h-index: 14)
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1, SJR: 1.167, h-index: 26)
Annals of Behavioral Medicine     Hybrid Journal   (Followers: 12, SJR: 2.112, h-index: 98)
Annals of Biomedical Engineering     Hybrid Journal   (Followers: 18, SJR: 1.182, h-index: 94)
Annals of Combinatorics     Hybrid Journal   (Followers: 3, SJR: 0.849, h-index: 15)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Dyslexia     Hybrid Journal   (Followers: 9, SJR: 0.857, h-index: 40)
Annals of Finance     Hybrid Journal   (Followers: 28, SJR: 0.686, h-index: 14)
Annals of Forest Science     Hybrid Journal   (Followers: 4, SJR: 0.929, h-index: 57)
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1, SJR: 1.136, h-index: 23)
Annals of Hematology     Hybrid Journal   (Followers: 14, SJR: 1.117, h-index: 62)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6, SJR: 0.593, h-index: 42)
Annals of Microbiology     Hybrid Journal   (Followers: 9, SJR: 0.402, h-index: 26)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 5, SJR: 0.68, h-index: 45)
Annals of Operations Research     Hybrid Journal   (Followers: 8, SJR: 1.186, h-index: 78)
Annals of Ophthalmology     Hybrid Journal   (Followers: 9)
Annals of Regional Science     Hybrid Journal   (Followers: 7, SJR: 0.405, h-index: 42)
Annals of Software Engineering     Hybrid Journal   (Followers: 12)
Annals of Solid and Structural Mechanics     Hybrid Journal   (Followers: 10, SJR: 0.553, h-index: 8)
Annals of Surgical Oncology     Hybrid Journal   (Followers: 11, SJR: 1.902, h-index: 127)
Annals of Telecommunications     Hybrid Journal   (Followers: 7, SJR: 0.315, h-index: 25)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.931, h-index: 31)
Antonie van Leeuwenhoek     Hybrid Journal   (Followers: 5, SJR: 0.992, h-index: 87)
Apidologie     Hybrid Journal   (Followers: 4, SJR: 1.14, h-index: 57)
APOPTOSIS     Hybrid Journal   (Followers: 8, SJR: 1.554, h-index: 87)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2, SJR: 0.354, h-index: 27)
Applications of Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.274, h-index: 20)
Applied Biochemistry and Biotechnology     Hybrid Journal   (Followers: 44, SJR: 0.575, h-index: 80)
Applied Biochemistry and Microbiology     Hybrid Journal   (Followers: 17, SJR: 0.267, h-index: 26)
Applied Categorical Structures     Hybrid Journal   (Followers: 2, SJR: 0.361, h-index: 21)
Applied Composite Materials     Hybrid Journal   (Followers: 47, SJR: 0.705, h-index: 35)
Applied Entomology and Zoology     Partially Free   (Followers: 2, SJR: 0.554, h-index: 34)
Applied Geomatics     Hybrid Journal   (Followers: 3, SJR: 0.323, h-index: 9)
Applied Geophysics     Hybrid Journal   (Followers: 7, SJR: 0.541, h-index: 13)
Applied Intelligence     Hybrid Journal   (Followers: 12, SJR: 0.777, h-index: 43)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 3, SJR: 0.358, h-index: 34)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4, SJR: 0.955, h-index: 33)
Applied Mathematics - A J. of Chinese Universities     Hybrid Journal   (SJR: 0.275, h-index: 8)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 4, SJR: 0.37, h-index: 26)
Applied Microbiology and Biotechnology     Hybrid Journal   (Followers: 61, SJR: 1.262, h-index: 161)
Applied Physics A     Hybrid Journal   (Followers: 7, SJR: 0.535, h-index: 121)
Applied Physics B: Lasers and Optics     Hybrid Journal   (Followers: 23, SJR: 0.983, h-index: 104)
Applied Psychophysiology and Biofeedback     Hybrid Journal   (Followers: 7, SJR: 0.677, h-index: 47)
Applied Research in Quality of Life     Hybrid Journal   (Followers: 10, SJR: 0.288, h-index: 15)
Applied Solar Energy     Hybrid Journal   (Followers: 17, SJR: 0.251, h-index: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4, SJR: 0.351, h-index: 9)
Aquaculture Intl.     Hybrid Journal   (Followers: 22, SJR: 0.613, h-index: 40)
Aquarium Sciences and Conservation     Hybrid Journal   (Followers: 1)
Aquatic Ecology     Hybrid Journal   (Followers: 30, SJR: 0.646, h-index: 44)
Aquatic Geochemistry     Hybrid Journal   (Followers: 3, SJR: 0.764, h-index: 39)
Aquatic Sciences     Hybrid Journal   (Followers: 12, SJR: 1.172, h-index: 53)
Arabian J. for Science and Engineering     Hybrid Journal   (Followers: 5, SJR: 0.345, h-index: 20)
Arabian J. of Geosciences     Hybrid Journal   (Followers: 1, SJR: 0.417, h-index: 16)
Archaeological and Anthropological Sciences     Hybrid Journal   (Followers: 21, SJR: 1.056, h-index: 15)
Archaeologies     Hybrid Journal   (Followers: 12, SJR: 0.397, h-index: 13)
Archiv der Mathematik     Hybrid Journal   (Followers: 1, SJR: 0.597, h-index: 29)
Archival Science     Hybrid Journal   (Followers: 52, SJR: 0.804, h-index: 22)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 7, SJR: 0.28, h-index: 15)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1, SJR: 0.946, h-index: 23)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (SJR: 4.091, h-index: 66)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4, SJR: 0.865, h-index: 40)
Archives and Museum Informatics     Hybrid Journal   (Followers: 120)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4, SJR: 2.841, h-index: 40)
Archives of Dermatological Research     Hybrid Journal   (Followers: 6, SJR: 0.9, h-index: 65)
Archives of Environmental Contamination and Toxicology     Hybrid Journal   (Followers: 10, SJR: 0.846, h-index: 84)
Archives of Gynecology and Obstetrics     Hybrid Journal   (Followers: 17, SJR: 0.695, h-index: 47)
Archives of Microbiology     Hybrid Journal   (Followers: 8, SJR: 0.702, h-index: 85)
Archives of Orthopaedic and Trauma Surgery     Hybrid Journal   (Followers: 8, SJR: 1.039, h-index: 56)
Archives of Osteoporosis     Hybrid Journal   (Followers: 2, SJR: 1.092, h-index: 13)
Archives of Sexual Behavior     Hybrid Journal   (Followers: 9, SJR: 1.198, h-index: 74)
Archives of Toxicology     Hybrid Journal   (Followers: 16, SJR: 1.595, h-index: 76)
Archives of Virology     Hybrid Journal   (Followers: 5, SJR: 1.086, h-index: 90)
Archives of Women's Mental Health     Hybrid Journal   (Followers: 13, SJR: 1.264, h-index: 50)
Archivio di Ortopedia e Reumatologia     Hybrid Journal  
Archivum Immunologiae et Therapiae Experimentalis     Hybrid Journal   (Followers: 2, SJR: 1.2, h-index: 42)
ArgoSpine News & J.     Hybrid Journal   (SJR: 0.102, h-index: 3)
Argumentation     Hybrid Journal   (Followers: 5, SJR: 0.295, h-index: 18)
Arid Ecosystems     Hybrid Journal   (Followers: 3)
Arkiv för Matematik     Hybrid Journal   (Followers: 1, SJR: 0.948, h-index: 22)
Arnold Mathematical J.     Hybrid Journal   (Followers: 1)
Arthropod-Plant Interactions     Hybrid Journal   (Followers: 1, SJR: 0.797, h-index: 17)
Arthroskopie     Hybrid Journal   (Followers: 1, SJR: 0.145, h-index: 8)
Artificial Intelligence and Law     Hybrid Journal   (Followers: 9, SJR: 0.288, h-index: 25)
Artificial Intelligence Review     Hybrid Journal   (Followers: 14, SJR: 0.948, h-index: 48)
Artificial Life and Robotics     Hybrid Journal   (Followers: 7, SJR: 0.231, h-index: 14)
Asia Europe J.     Hybrid Journal   (Followers: 4, SJR: 0.247, h-index: 9)
Asia Pacific Education Review     Hybrid Journal   (Followers: 9, SJR: 0.371, h-index: 17)
Asia Pacific J. of Management     Hybrid Journal   (Followers: 12, SJR: 1.676, h-index: 50)
Asia-Pacific Education Researcher     Hybrid Journal   (Followers: 11, SJR: 0.353, h-index: 13)
Asia-Pacific Financial Markets     Hybrid Journal   (Followers: 2, SJR: 0.19, h-index: 15)
Asia-Pacific J. of Atmospheric Sciences     Hybrid Journal   (Followers: 20, SJR: 1.006, h-index: 14)
Asian Business & Management     Hybrid Journal   (Followers: 7, SJR: 0.41, h-index: 10)
Asian J. of Business Ethics     Hybrid Journal   (Followers: 7)
Asian J. of Criminology     Hybrid Journal   (Followers: 5, SJR: 0.263, h-index: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 2, SJR: 0.681, h-index: 15)
AStA Wirtschafts- und Sozialstatistisches Archiv     Hybrid Journal   (Followers: 5, SJR: 0.195, h-index: 5)
ästhetische dermatologie & kosmetologie     Full-text available via subscription  
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 21, SJR: 4.511, h-index: 44)
Astronomy Letters     Hybrid Journal   (Followers: 20, SJR: 0.58, h-index: 30)

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Journal Cover Archive for Rational Mechanics and Analysis
  [SJR: 4.091]   [H-I: 66]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0673 - ISSN (Online) 0003-9527
   Published by Springer-Verlag Homepage  [2345 journals]
  • Homogenization of the Brush Problem with a Source Term in L 1
    • Authors: Antonio Gaudiello; Olivier Guibé; François Murat
      Pages: 1 - 64
      Abstract: We consider a domain which has the form of a brush in 3D or the form of a comb in 2D, i.e. an open set which is composed of cylindrical vertical teeth distributed over a fixed basis. All the teeth have a similar fixed height; their cross sections can vary from one tooth to another and are not supposed to be smooth; moreover the teeth can be adjacent, i.e. they can share parts of their boundaries. The diameter of every tooth is supposed to be less than or equal to \({\varepsilon}\) , and the asymptotic volume fraction of the teeth (as \({\varepsilon}\) tends to zero) is supposed to be bounded from below away from zero, but no periodicity is assumed on the distribution of the teeth. In this domain we study the asymptotic behavior (as \({\varepsilon}\) tends to zero) of the solution of a second order elliptic equation with a zeroth order term which is bounded from below away from zero, when the homogeneous Neumann boundary condition is satisfied on the whole of the boundary. First, we revisit the problem where the source term belongs to L 2. This is a classical problem, but our homogenization result takes place in a geometry which is more general that the ones which have been considered before. Moreover we prove a corrector result which is new. Then, we study the case where the source term belongs to L 1. Working in the framework of renormalized solutions and introducing a definition of renormalized solutions for degenerate elliptic equations where only the vertical derivative is involved (such a definition is new), we identify the limit problem and prove a corrector result.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1079-2
      Issue No: Vol. 225, No. 1 (2017)
       
  • A Measure and Orientation Preserving Homeomorphism with Approximate
           Jacobian Equal −1 Almost Everywhere
    • Authors: Paweł Goldstein; Piotr Hajłasz
      Pages: 65 - 88
      Abstract: We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit n-dimensional cube onto itself, whose Jacobian is equal to −1 almost everywhere. Moreover, we prove that our homeomorphism can be uniformly approximated by orientation and measure preserving diffeomorphisms.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1085-4
      Issue No: Vol. 225, No. 1 (2017)
       
  • The Elastic Trefoil is the Doubly Covered Circle
    • Authors: Henryk Gerlach; Philipp Reiter; Heiko von der Mosel
      Pages: 89 - 139
      Abstract: To describe the behavior of knotted loops of springy wire with an elementary mathematical model we minimize the integral of squared curvature, \({E = \int \varkappa^2}\) , together with a small multiple of ropelength \({\mathcal{R}}\) = length/thickness in order to penalize selfintersection. Our main objective is to characterize all limit configurations of energy minimizers of the total energy \({E_{\vartheta} \equiv E + \vartheta \mathcal{R}}\) as \({\vartheta}\) tends to zero. For short, these limit configurations will be referred to as elastic knots. The elastic unknot turns out to be the once covered circle with squared curvature energy \({(2\pi)^2}\) . For all (non-trivial) knot classes for which the natural lower bound \({(4\pi)^2}\) on E is sharp, the respective elastic knot is the doubly covered circle. We also derive a new characterization of two-bridge torus knots in terms of E, proving that the only knot classes for which the lower bound \({(4\pi)^2}\) on E is sharp are the \({(2,b)}\) -torus knots for odd b with \({ b \ge 3}\) (containing the trefoil knot class). In particular, the elastic trefoil knot is the doubly covered circle.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1100-9
      Issue No: Vol. 225, No. 1 (2017)
       
  • Global Existence and Asymptotic Behavior of Affine Motion of 3D Ideal
           Fluids Surrounded by Vacuum
    • Authors: Thomas C. Sideris
      Pages: 141 - 176
      Abstract: The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in \({{\rm GL}^+(3, \mathbb{R})}\) . The evolution of the fluid domain is described by a family of ellipsoids whose diameter grows at a rate proportional to time. Upon rescaling to a fixed diameter, the asymptotic limit of the fluid ellipsoid is determined by a positive semi-definite quadratic form of rank r = 1, 2, or 3, corresponding to the asymptotic degeneration of the ellipsoid along 3−r of its principal axes. In the compressible case, the asymptotic limit has rank r = 3, and asymptotic completeness holds, when the adiabatic index \({\gamma}\) satisfies \({4/3 < \gamma < 2}\) . The number of possible degeneracies, 3−r, increases with the value of the adiabatic index \({\gamma}\) . In the incompressible case, affine motion reduces to geodesic flow in \({{\rm SL}(3, \mathbb{R})}\) with the Euclidean metric. For incompressible affine swirling flow, there is a structural instability. Generically, when the vorticity is nonzero, the domains degenerate along only one axis, but the physical vacuum boundary condition fails over a finite time interval. The rescaled fluid domains of irrotational motion can collapse along two axes.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1106-3
      Issue No: Vol. 225, No. 1 (2017)
       
  • A Temperature-Dependent Phase-Field Model for Phase Separation and Damage
    • Authors: Christian Heinemann; Christiane Kraus; Elisabetta Rocca; Riccarda Rossi
      Pages: 177 - 247
      Abstract: In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature concerning phase separation and damage processes in elastic media, in our model we encompass thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More particularly, we prove the existence of “entropic weak solutions”, resorting to a solvability concept first introduced in Feireisl (Comput Math Appl 53:461–490, 2007) in the framework of Fourier–Navier–Stokes systems and then recently employed in Feireisl et al. (Math Methods Appl Sci 32:1345–1369, 2009) and Rocca and Rossi (Math Models Methods Appl Sci 24:1265–1341, 2014) for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1102-7
      Issue No: Vol. 225, No. 1 (2017)
       
  • A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear
           Elastic Energy in Two Dimensions
    • Authors: Jonathan J. Bevan
      Pages: 249 - 285
      Abstract: We prove the local Hölder continuity of strong local minimizers of the stored energy functional $$E(u)=\int_{\Omega}\lambda \nabla u ^{2}+h({\rm det} \nabla u)\,{\rm d}x$$ subject to a condition of ‘positive twist’. The latter turns out to be equivalent to requiring that u maps circles to suitably star-shaped sets. The convex function h(s) grows logarithmically as \({s\to 0+}\) , linearly as \({s \to +\infty}\) , and satisfies \({h(s)=+\infty}\) if \({s \leqq 0}\) . These properties encode a constitutive condition which ensures that material does not interpenetrate during a deformation and is one of the principal obstacles to proving the regularity of local or global minimizers. The main innovation is to prove that if a local minimizer has positive twist a.e. on a ball then an Euler-Lagrange type inequality holds and a Caccioppoli inequality can be derived from it. The claimed Hölder continuity then follows by adapting some well-known elliptic regularity theory. We also demonstrate the regularizing effect that the term \({\int_{\Omega} h({\rm det} \nabla u)\,{\rm d}x}\) can have by analysing the regularity of local minimizers in the class of ‘shear maps’. In this setting a more easily verifiable condition than that of positive twist is imposed, with the result that local minimizers are Hölder continuous.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1104-5
      Issue No: Vol. 225, No. 1 (2017)
       
  • On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk
    • Authors: Yasunori Maekawa
      Pages: 287 - 374
      Abstract: We study the stability of some exact stationary solutions to the two-dimensional Navier–Stokes equations in an exterior domain to the unit disk. These stationary solutions are known as a simple model of the flow around a rotating obstacle, while their stability has been open due to the difficulty arising from their spatial decay in a scale-critical order. In this paper we affirmatively settle this problem for small solutions. That is, we will show that if these exact solutions are small enough then they are asymptotically stable with respect to small L 2 perturbations.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1105-4
      Issue No: Vol. 225, No. 1 (2017)
       
  • Global Well-Posedness of the Boltzmann Equation with Large Amplitude
           Initial Data
    • Authors: Renjun Duan; Feimin Huang; Yong Wang; Tong Yang
      Pages: 375 - 424
      Abstract: The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new \({L^\infty_xL^1_{v}\cap L^\infty_{x,v}}\) approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted \({L^\infty}\) norm under some smallness condition on the \({L^1_xL^\infty_v}\) norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the \({L^\infty_{x,v}}\) norm with explicit rates of convergence are also studied.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1107-2
      Issue No: Vol. 225, No. 1 (2017)
       
  • A Derivation of Linearized Griffith Energies from Nonlinear Models
    • Authors: Manuel Friedrich
      Pages: 425 - 467
      Abstract: We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in a brittle fracture via \({\Gamma}\) -convergence. The convergence is given in terms of rescaled displacement fields measuring the distance of deformations from piecewise rigid motions. The configurations of the limiting model consist of partitions of the material, corresponding piecewise rigid deformations and displacement fields which are defined separately on each component of the cracked body. Apart from the linearized Griffith energy the limiting functional also comprises the segmentation energy, which is necessary to disconnect the parts of the specimen.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1108-1
      Issue No: Vol. 225, No. 1 (2017)
       
  • Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger
           Equation on $${\mathbb{R}^3}$$ R 3
    • Authors: Rowan Killip; Tadahiro Oh; Oana Pocovnicu; Monica Vişan
      Pages: 469 - 548
      Abstract: We consider the cubic–quintic nonlinear Schrödinger equation: $$i\partial_t u = -\Delta u - u ^2u + u ^4u.$$ In the first part of the paper, we analyze the one-parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass/energy curve. Additionally, we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one-parameter family of inequalities of Gagliardo–Nirenberg type. Building on this work, in the latter part of the paper we prove that scattering holds for solutions belonging to the region \({{\mathcal{R}}}\) of the mass/energy plane where the virial is positive. We show that this region is partially bounded by solitons also by rescalings of solitons (which are not soliton solutions in their own right). The discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial-based methodology.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1109-0
      Issue No: Vol. 225, No. 1 (2017)
       
  • On the Liouville Type Theorems for Self-Similar Solutions to the
           Navier–Stokes Equations
    • Authors: Dongho Chae; Jörg Wolf
      Pages: 549 - 572
      Abstract: We prove Liouville type theorems for the self-similar solutions to the Navier–Stokes equations. One of our results generalizes the previous ones by Nečas–Ru̇žička–Šverák and Tsai. Using a Liouville type theorem, we also remove a scenario of asymptotically self-similar blow-up for the Navier–Stokes equations with the profile belonging to \({L^{p, \infty} (\mathbb{R}^3)}\) with \({p > \frac{3}{2}}\) .
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1110-7
      Issue No: Vol. 225, No. 1 (2017)
       
  • From the Q-Tensor Flow for the Liquid Crystal to the Harmonic Map Flow
    • Abstract: In this paper, we consider the solutions of the relaxed Q-tensor flow in \({\mathbb{R}^3}\) with small parameter \({\epsilon}\) . We show that the limiting map is the so-called harmonic map flow. As a consequence, we present a new proof for the global existence of a weak solution for the harmonic map flow in three dimensions as in [18, 23], where the Ginzburg–Landau approximation approach was used.
      PubDate: 2017-08-01
       
  • The Euler–Maxwell System for Electrons: Global Solutions in 2 D
    • Abstract: A basic model for describing plasma dynamics is given by the Euler–Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the “one-fluid” Euler–Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background. In 2 dimensions our global solutions have relatively slow (strictly less than 1/t) pointwise decay and the system has a large (codimension 1) set of quadratic time resonances. The issue in such a situation is to solve the “division problem”. To control the solutions we use a combination of improved energy estimates in the Fourier space, an L 2 bound on an oscillatory integral operator, and Fourier analysis of the Duhamel formula.
      PubDate: 2017-08-01
       
  • Multiphase Solutions to the Vector Allen–Cahn Equation: Crystalline and
           Other Complex Symmetric Structures
    • Abstract: We present a systematic study of entire symmetric solutions \({u : \mathbb{R}^n \rightarrow\mathbb{R}^m}\) of the vector Allen–Cahn equation $$\Delta u - W_u(u) = 0 \quad\text{for all}\quad x \in \mathbb{R}^n,$$ where \({W:\mathbb{R}^m \rightarrow \mathbb{R}}\) is smooth, symmetric, nonnegative with a finite number of zeros, and where \({ W_u= (\partial W / \partial u_1,\dots,\partial W / \partial u_m)^{\top}}\) . We introduce a general notion of equivariance with respect to a homomorphism \({f:G\rightarrow\Gamma}\) ( \({G, \Gamma}\) reflection groups) and prove two abstract results, concerning the cases of G finite and G discrete, for the existence of equivariant solutions. Our approach is variational and based on a mapping property of the parabolic vector Allen–Cahn equation and on a pointwise estimate for vector minimizers.
      PubDate: 2017-08-01
       
  • On Slowly Rotating Axisymmetric Solutions of the Euler–Poisson
           Equations
    • Abstract: We construct stationary axisymmetric solutions of the Euler–Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity when the adiabatic exponent \({\gamma}\) belongs to \({(\frac65,\frac32]}\) . The problem is formulated as a nonlinear integral equation, and is solved by an iteration technique. By this method, not only do we get the existence, but we also clarify properties of the solutions such as the physical vacuum condition and the oblateness of the star surface.
      PubDate: 2017-08-01
       
  • On the Asymptotic Stability of Stationary Solutions of the Inviscid
           Incompressible Porous Medium Equation
    • Abstract: We study the stability of stationary solutions of the two dimensional inviscid incompressible porous medium equation (IPM). We show that solutions which are near certain stable stationary solutions must converge as t → ∞ to a stationary solution of the IPM equation. It turns out that linearizing the IPM equation about certain stable stationary solutions gives a non-local partial damping mechanism. On the torus, the linearized problem has a very large set of stationary (undamped) modes. This makes the problem of long-time behavior more difficult since there is the possibility of a cascading non-linear growth along the stationary modes of the linearized problem. We solve this by, more or less, doing a second linearization around the undamped modes, exploiting a special non-linear structure, and showing that the stationary modes can be controlled.
      PubDate: 2017-08-01
       
  • On the Existence of Integrable Solutions to Nonlinear Elliptic Systems and
           Variational Problems with Linear Growth
    • Abstract: We investigate the properties of certain elliptic systems leading, a priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic radial structure, then the solution can in fact be understood as a standard weak solution, with one proviso: analogously to the case of minimal surface equations, the attainment of the boundary value is penalized by a measure supported on (a subset of) the boundary, which, for the class of problems under consideration here, is the part of the boundary where a Neumann boundary condition is imposed.
      PubDate: 2017-08-01
       
  • Optimal Quantitative Estimates in Stochastic Homogenization for Elliptic
           Equations in Nondivergence Form
    • Abstract: We prove quantitative estimates for the stochastic homogenization of linear uniformly elliptic equations in nondivergence form. Under strong independence assumptions on the coefficients, we obtain optimal estimates on the subquadratic growth of the correctors with stretched exponential-type bounds in probability. Like the theory of Gloria and Otto (Ann Probab 39(3):779–856, 2011; Ann Appl Probab 22(1):1–28, 2012) for divergence form equations, the arguments rely on nonlinear concentration inequalities combined with certain estimates on the Green’s functions and derivative bounds on the correctors. We obtain these analytic estimates by developing a C 1,1 regularity theory down to microscopic scale, which is of independent interest and is inspired by the C 0,1 theory introduced in the divergence form case by the first author and Smart (Ann Sci Éc Norm Supér (4) 49(2):423–481, 2016).
      PubDate: 2017-08-01
       
  • Gevrey Smoothing for Weak Solutions of the Fully Nonlinear Homogeneous
           Boltzmann and Kac Equations Without Cutoff for Maxwellian Molecules
    • Abstract: It has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties to the fractional Laplacian. This has led to the hope that the homogenous Boltzmann equation enjoys similar regularity properties to the heat equation with a fractional Laplacian. In particular, the weak solution of the fully nonlinear non-cutoff homogenous Boltzmann equation with initial datum in \({L^1_2(\mathbb{R}^d)\cap L {\rm log} L(\mathbb{R}^d)}\) , i.e., finite mass, energy and entropy, should immediately become Gevrey regular for strictly positive times. We prove this conjecture for Maxwellian molecules.
      PubDate: 2017-08-01
       
  • Simple Choreographies of the Planar Newtonian N -Body Problem
    • Abstract: In the N-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian N-body problem with equal masses, N ≧ 3, there are at least 2 N-3 +  2[(N-3)/2] different main simple choreographies. This confirms a conjecture given by Chenciner et al. (Geometry, mechanics, and dynamics. Springer, New York, pp 287–308, 2002). All the simple choreoagraphies we prove belong to the linear chain family.
      PubDate: 2017-08-01
       
 
 
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