for Journals by Title or ISSN
for Articles by Keywords
help
  Subjects -> MATHEMATICS (Total: 910 journals)
    - APPLIED MATHEMATICS (75 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (677 journals)
    - MATHEMATICS (GENERAL) (41 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (78 journals)

MATHEMATICS (677 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 6)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 11)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 3)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 6)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 7)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 10)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)

        1 2 3 4 | Last

Journal Cover Calculus of Variations and Partial Differential Equations
  [SJR: 2.455]   [H-I: 44]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0835 - ISSN (Online) 0944-2669
   Published by Springer-Verlag Homepage  [2355 journals]
  • Improved stability of optimal traffic paths
    • Authors: Maria Colombo; Antonio De Rosa; Andrea Marchese
      Abstract: Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree, and the nervous or cardiovascular systems. Given a flow (traffic path) that transports a given measure \(\mu ^-\) onto a target measure \(\mu ^+\) , along a 1-dimensional network, the transportation cost per unit length is supposed in these models to be proportional to a concave power \(\alpha \in (0,1)\) of the intensity of the flow. In this paper we address an open problem in the book Optimal transportation networks by Bernot, Caselles and Morel and we improve the stability for optimal traffic paths in the Euclidean space \(\mathbb {R}^d\) , with respect to variations of the given measures \((\mu ^-,\mu ^+)\) , which was known up to now only for \(\alpha >1-\frac{1}{d}\) . We prove it for exponents \(\alpha >1-\frac{1}{d-1}\) [in particular, for every \(\alpha \in (0,1)\) when \(d=2\) ], for a fairly large class of measures \(\mu ^+\) and \(\mu ^-\) .
      PubDate: 2018-01-19
      DOI: 10.1007/s00526-017-1299-1
      Issue No: Vol. 57, No. 1 (2018)
       
  • Fractional Sobolev metrics on spaces of immersed curves
    • Authors: Martin Bauer; Martins Bruveris; Boris Kolev
      Abstract: Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves \(\mathrm {Imm}(\mathrm {S}^{1},\mathbb {R}^d)\) and on its Sobolev completions \({\mathcal {I}}^{q}(\mathrm {S}^{1},{\mathbb {R}}^{d})\) . We prove local well-posedness of the geodesic equations both on the Banach manifold \({\mathcal {I}}^{q}(\mathrm {S}^{1},{\mathbb {R}}^{d})\) and on the Fréchet-manifold \(\mathrm {Imm}(\mathrm {S}^{1},\mathbb {R}^d)\) provided the order of the metric is greater or equal to one. In addition we show that the \(H^s\) -metric induces a strong Riemannian metric on the Banach manifold \({\mathcal {I}}^{s}(\mathrm {S}^{1},{\mathbb {R}}^{d})\) of the same order s, provided \(s>\frac{3}{2}\) . These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group.
      PubDate: 2018-01-13
      DOI: 10.1007/s00526-018-1300-7
      Issue No: Vol. 57, No. 1 (2018)
       
  • Polyconvexity for functions of a system of closed differential forms
    • Authors: M. Šilhavý
      Abstract: This paper deals with the weakened convexity properties, mult. ext. quasiconvexity, mult. ext. one convexity, and mult. ext. polyconvexity, for integral functionals of the form $$\begin{aligned} I(\omega _1,\ldots ,\omega _s) = \int _\Omega f(\omega _1,\ldots ,\omega _s) dx \end{aligned}$$ where \(\omega _1,\ldots ,\omega _s\) are closed differential forms on a bounded open set \(\Omega \subset {\mathbb {R}}^n\) . The main results of the paper are explicit descriptions of mult. ext. quasiaffine and mult ext. polyconvex functions. It turns out that these two classes consist, respectively, of linear and convex combinations of the set of all wedge products of exterior powers of the forms \(\omega _1,\ldots ,\omega _s\) . Thus, for example, a function \(f=f(\omega _1,\ldots ,\omega _s)\) is mult. ext. polyconvex if and only if $$\begin{aligned} f(\omega _1,\ldots ,\omega _s) = \Phi (\ldots ,\omega _1^{q_1}\wedge \cdots \wedge \omega _s^{q_s},\ldots ) \end{aligned}$$ where \(q_1,\ldots ,q_s\) ranges a finite set of integers and \(\Phi \) is a convex function. An existence theorem for the minimum energy state is proved for mult. ext. polyconvex integrals. The polyconvexity in the calculus of variations and nonlinear elasticity are particular cases of mult. ext. polyconvexity. Our main motivation comes from electro-magneto-elastic interactions in continuous bodies. There the mult. ext. polyconvexity takes the form determined by an involved direct calculation in an earlier paper of the author (Šilhavý in Math Mech Solids, 2017. http://journals.sagepub.com/doi/metrics/10.1177/1081286517696536).
      PubDate: 2018-01-10
      DOI: 10.1007/s00526-017-1298-2
      Issue No: Vol. 57, No. 1 (2018)
       
  • Neumann heat flow and gradient flow for the entropy on non-convex domains
    • Authors: Janna Lierl; Karl-Theodor Sturm
      Abstract: For large classes of non-convex subsets Y in \(\mathbb R^n\) or in Riemannian manifolds (M, g) or in RCD-spaces (X, d, m) we prove that the gradient flow for the Boltzmann entropy on the restricted metric measure space \((Y,d_Y,m_Y)\) exists—despite the fact that the entropy is not semiconvex—and coincides with the heat flow on Y with Neumann boundary conditions.
      PubDate: 2018-01-06
      DOI: 10.1007/s00526-017-1292-8
      Issue No: Vol. 57, No. 1 (2018)
       
  • Discrete minimisers are close to continuum minimisers for the interaction
           energy
    • Authors: J. A. Cañizo; F. S. Patacchini
      Abstract: Under suitable technical conditions we show that minimisers of the discrete interaction energy for attractive-repulsive potentials converge to minimisers of the corresponding continuum energy as the number of particles goes to infinity. We prove that the discrete interaction energy \(\Gamma \) -converges in the narrow topology to the continuum interaction energy. As an important part of the proof we study support and regularity properties of discrete minimisers: we show that continuum minimisers belong to suitable Morrey spaces and we introduce the set of empirical Morrey measures as a natural iscrete analogue containing all the discrete minimisers.
      PubDate: 2018-01-02
      DOI: 10.1007/s00526-017-1289-3
      Issue No: Vol. 57, No. 1 (2018)
       
  • Compactness analysis for free boundary minimal hypersurfaces
    • Authors: Lucas Ambrozio; Alessandro Carlotto; Ben Sharp
      Abstract: We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control.
      PubDate: 2017-12-26
      DOI: 10.1007/s00526-017-1281-y
      Issue No: Vol. 57, No. 1 (2017)
       
  • Bifurcations from the orbit of solutions of the Neumann problem
    • Authors: Anna Gołȩbiewska; Joanna Kluczenko; Piotr Stefaniak
      Abstract: The purpose of this paper is to study weak solutions of a nonlinear Neumann problem considered on a ball. Assuming that the potential is invariant, we consider an orbit of critical points, i.e. we do not assume that critical points are isolated. We apply techniques of equivariant analysis to examine bifurcations from the orbits of trivial solutions. We formulate sufficient conditions for local and global bifurcations, in terms of the right-hand side of the system and eigenvalues of the Laplace operator. Moreover, we characterise orbits at which global symmetry breaking phenomena occur.
      PubDate: 2017-12-26
      DOI: 10.1007/s00526-017-1285-7
      Issue No: Vol. 57, No. 1 (2017)
       
  • Existence and phase separation of entire solutions to a pure critical
           competitive elliptic system
    • Authors: Mónica Clapp; Angela Pistoia
      Abstract: We establish the existence of a positive fully nontrivial solution (u, v) to the weakly coupled elliptic system $$\begin{aligned} {\left\{ \begin{array}{ll} -\,\Delta u=\mu _{1} u ^{{2}^{*}-2}u+\lambda \alpha u ^{\alpha -2} v ^{\beta }u,\\ -\,\Delta v=\mu _{2} v ^{{2}^{*}-2}v+\lambda \beta u ^{\alpha } v ^{\beta {-2} }v,\\ u,v\in D^{1,2}({\mathbb {R}}^{N}), \end{array}\right. } \end{aligned}$$ where \(N\ge 4,\) \(2^{*}:=\frac{2N}{N-2}\) is the critical Sobolev exponent, \(\alpha ,\beta \in (1,2],\) \(\alpha +\beta =2^{*},\) \(\mu _{1},\mu _{2}>0,\) and \(\lambda <0.\) We show that these solutions exhibit phase separation as \(\lambda \rightarrow -\,\infty ,\) and we give a precise description of their limit domains. If \(\mu _{1}=\mu _{2}\) and \(\alpha =\beta \) , we prove that the system has infinitely many fully nontrivial solutions, which are not conformally equivalent.
      PubDate: 2017-12-26
      DOI: 10.1007/s00526-017-1283-9
      Issue No: Vol. 57, No. 1 (2017)
       
  • Gradient flow for the Boltzmann entropy and Cheeger’s energy on
           time-dependent metric measure spaces
    • Authors: Eva Kopfer
      Abstract: We introduce notions of dynamic gradient flows on time-dependent metric spaces as well as on time-dependent Hilbert spaces. We prove existence of solutions for a class of time-dependent energy functionals in both settings. In particular, in the case when each underlying space satisfies a lower Ricci curvature bound in the sense of Lott, Sturm and Villani, we provide time-discrete approximations of the time-dependent heat flows introduced in Kopfer and Sturm (Heat flows on time-dependent metric measure spaces and super-Ricci flows, 2017. arXiv:1611.02570).
      PubDate: 2017-12-23
      DOI: 10.1007/s00526-017-1287-5
      Issue No: Vol. 57, No. 1 (2017)
       
  • Distances between classes in $$W^{1,1}(\Omega ;{\mathbb {S}}^{1})$$ W 1 ,
           1 ( Ω ; S 1 )
    • Authors: Haim Brezis; Petru Mironescu; Itai Shafrir
      Abstract: We introduce an equivalence relation on the space \(W^{1,1}(\Omega ;{\mathbb {S}}^1)\) which classifies maps according to their “topological singularities”. We establish sharp bounds for the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. Similar questions are examined for the space \(W^{1,p}(\Omega ;{\mathbb {S}}^1)\) when \(p>1\) .
      PubDate: 2017-12-22
      DOI: 10.1007/s00526-017-1280-z
      Issue No: Vol. 57, No. 1 (2017)
       
  • Flatness implies smoothness for solutions of the porous medium equation
    • Authors: Clemens Kienzler; Herbert Koch; Juan Luis Vázquez
      Abstract: One of the major problems in the theory of the porous medium equation \(\partial _t\rho =\Delta _x\rho ^m,\,m > 1\) , is the regularity of the solutions \(\rho (t,x)\ge 0\) and the free boundaries \(\Gamma =\partial \{(t,x): \rho >0\}\) . Here we assume flatness of the solution and derive \(C^\infty \) regularity of the interface after a small time, as well as \(C^\infty \) regularity of the solution in the positivity set and up to the free boundary for some time interval. The proof starts from Caffarelli’s blueprint of an improvement of flatness by rescaling, and combines it with the Carleson measure approach applied to the degenerate subelliptic equation satisfied by the pressure of the porous medium equation in transformed coordinates. The improvement of flatness finally hinges on Gaussian estimates for the subelliptic problem. We use these facts to prove the following eventual regularity result: solutions defined in the whole space with compactly supported initial data are smooth after a finite time \(T_r\) that depends on \(\rho _0\) . More precisely, we prove that for \(t \ge T_r\) the pressure \(\rho ^{m-1}\) is \(C^\infty \) in the positivity set and up to the free boundary, which is a \(C^\infty \) hypersurface. Moreover, \(T_r\) can be estimated in terms of only the initial mass and the initial support radius. This regularity result eliminates the assumption of non-degeneracy on the initial data that has been carried on for decades in the literature. Let us recall that regularization for small times is false, and that as \(t\rightarrow \infty \) the solution increasingly resembles a Barenblatt function and the support looks like a ball.
      PubDate: 2017-12-22
      DOI: 10.1007/s00526-017-1296-4
      Issue No: Vol. 57, No. 1 (2017)
       
  • The Riesz transform and quantitative rectifiability for general Radon
           measures
    • Authors: Daniel Girela-Sarrión; Xavier Tolsa
      Abstract: In this paper we show that if \(\mu \) is a Borel measure in \({{\mathbb {R}}}^{n+1}\) with growth of order n, such that the n-dimensional Riesz transform \({{\mathcal {R}}}_\mu \) is bounded in \(L^2(\mu )\) , and \(B\subset {{\mathbb {R}}}^{n+1}\) is a ball with \(\mu (B)\approx r(B)^n\) such that: there is some n-plane L passing through the center of B such that for some \(\delta >0\) small enough, it holds $$\begin{aligned}\int _B \frac{\mathrm{dist}(x,L)}{r(B)}\,d\mu (x)\le \delta \,\mu (B),\end{aligned}$$ for some constant \({\varepsilon }>0\) small enough, $$\begin{aligned}\int _{B} {{\mathcal {R}}}_\mu 1(x) - m_{\mu ,B}({{\mathcal {R}}}_\mu 1) ^2\,d\mu (x) \le {\varepsilon }\,\mu (B),\end{aligned}$$ where \(m_{\mu ,B}({{\mathcal {R}}}_\mu 1)\) stands for the mean of \({{\mathcal {R}}}_\mu 1\) on B with respect to \(\mu \) , then there exists a uniformly n-rectifiable set \(\Gamma \) , with \(\mu (\Gamma \cap B)\gtrsim \mu (B)\) , and such that \(\mu _\Gamma \) is absolutely continuous with respect to \({{\mathcal {H}}}^n _\Gamma \) . This result is an essential tool to solve an old question on a two phase problem for harmonic measure in subsequent papers by Azzam, Mourgoglou, Tolsa, and Volberg.
      PubDate: 2017-12-22
      DOI: 10.1007/s00526-017-1294-6
      Issue No: Vol. 57, No. 1 (2017)
       
  • On the global well-posedness of 3-D axi-symmetric Navier–Stokes system
           with small swirl component
    • Authors: Yanlin Liu; Ping Zhang
      Abstract: In this paper, we prove the local well-posedness of 3-D axi-symmetric Navier–Stokes system with initial data in the critical Lebesgue spaces. We also obtain the global well-posedness result with small initial data. Furthermore, with the initial swirl component of the velocity being sufficiently small in the almost critical spaces, we can still prove the global well-posedness of the system.
      PubDate: 2017-12-22
      DOI: 10.1007/s00526-017-1288-4
      Issue No: Vol. 57, No. 1 (2017)
       
  • A three-dimensional symmetry result for a phase transition equation in the
           genuinely nonlocal regime
    • Authors: Serena Dipierro; Alberto Farina; Enrico Valdinoci
      Abstract: We consider bounded solutions of the nonlocal Allen–Cahn equation $$\begin{aligned} (-\Delta )^s u=u-u^3\qquad { \text{ in } }\mathbb {R}^3, \end{aligned}$$ under the monotonicity condition  \(\partial _{x_3}u>0\) and in the genuinely nonlocal regime in which  \(s\in \left( 0,\frac{1}{2}\right) \) . Under the limit assumptions $$\begin{aligned} \lim _{x_n\rightarrow -\infty } u(x',x_n)=-1\quad { \text{ and } }\quad \lim _{x_n\rightarrow +\infty } u(x',x_n)=1, \end{aligned}$$ it has been recently shown in Dipierro et al. (Improvement of flatness for nonlocal phase transitions, 2016) that u is necessarily 1D, i.e. it depends only on one Euclidean variable. The goal of this paper is to obtain a similar result without assuming such limit conditions. This type of results can be seen as nonlocal counterparts of the celebrated conjecture formulated by De Giorgi (Proceedings of the international meeting on recent methods in nonlinear analysis (Rome, 1978), Pitagora, Bologna, pp 131–188, 1979).
      PubDate: 2017-12-22
      DOI: 10.1007/s00526-017-1295-5
      Issue No: Vol. 57, No. 1 (2017)
       
  • $$T_5$$ T 5 -Configurations and non-rigid sets of matrices
    • Authors: Clemens Förster; László Székelyhidi
      Abstract: In 2003 B. Kirchheim-D. Preiss constructed a Lipschitz map in the plane with 5 incompatible gradients, where incompatibility refers to the condition that no two of the five matrices are rank-one connected. The construction is via the method of convex integration and relies on a detailed understanding of the rank-one geometry resulting from a specific set of five matrices. The full computation of the rank-one convex hull for this specific set was later carried out in 2010 by W. Pompe in Calc. Var. PDE 37(3–4):461–473, (2010) by delicate geometric arguments. For more general sets of matrices a full computation of the rank-one convex hull is clearly out of reach. Therefore, in this short note we revisit the construction and propose a new, in some sense generic method for deciding whether convex integration for a given set of matrices can be carried out, which does not require the full computation of the rank-one convex hull.
      PubDate: 2017-12-22
      DOI: 10.1007/s00526-017-1293-7
      Issue No: Vol. 57, No. 1 (2017)
       
  • Quasistatic evolution in non-associative plasticity revisited
    • Authors: G. A. Francfort; M. G. Mora
      Abstract: The mathematical treatment of evolutionary non-associative elasto-plasticity is still in its infancy. In particular, all existence results thus far rely on a spatially mollified stress admissibility constraint. Further, the evolution is formulated in a rescaled time from which it is very difficult to infer any useful information on the “real” time evolution. We propose a causal spatio-temporal mollification of the stress admissibility constraint that, while no more far-fetched than a purely spatial one, produces a more elegant and complete evolution for such models, and this in the “real” time variable.
      PubDate: 2017-12-21
      DOI: 10.1007/s00526-017-1284-8
      Issue No: Vol. 57, No. 1 (2017)
       
  • A concave–convex problem with a variable operator
    • Authors: Alexis Molino; Julio D. Rossi
      Abstract: We study the following elliptic problem \(-A(u) = \lambda u^q\) with Dirichlet boundary conditions, where \(A(u) (x) = \Delta u (x) \chi _{D_1} (x)+ \Delta _p u(x) \chi _{D_2}(x)\) is the Laplacian in one part of the domain, \(D_1\) , and the p-Laplacian (with \(p>2\) ) in the rest of the domain, \(D_2 \) . We show that this problem exhibits a concave–convex nature for \(1<q<p-1\) . In fact, we prove that there exists a positive value \(\lambda ^*\) such that the problem has no positive solution for \(\lambda > \lambda ^*\) and a minimal positive solution for \(0<\lambda < \lambda ^*\) . If in addition we assume that p is subcritical, that is, \(p<2N/(N-2)\) then there are at least two positive solutions for almost every \(0<\lambda < \lambda ^*\) , the first one (that exists for all \(0<\lambda < \lambda ^*\) ) is obtained minimizing a suitable functional and the second one (that is proven to exist for almost every \(0<\lambda < \lambda ^*\) ) comes from an appropriate (and delicate) mountain pass argument.
      PubDate: 2017-12-21
      DOI: 10.1007/s00526-017-1291-9
      Issue No: Vol. 57, No. 1 (2017)
       
  • On Lipschitz continuity of solutions of hyperbolic Poisson’s
           equation
    • Authors: Jiaolong Chen; Manzi Huang; Antti Rasila; Xiantao Wang
      Abstract: In this paper, we investigate solutions of the hyperbolic Poisson equation \(\Delta _{h}u(x)=\psi (x)\) , where \(\psi \in L^{\infty }(\mathbb {B}^{n}, {\mathbb R}^n)\) and $$\begin{aligned} \Delta _{h}u(x)= (1- x ^2)^2\Delta u(x)+2(n-2)\left( 1- x ^2\right) \sum _{i=1}^{n} x_{i} \frac{\partial u}{\partial x_{i}}(x) \end{aligned}$$ is the hyperbolic Laplace operator in the n-dimensional space \(\mathbb {R}^n\) for \(n\ge 2\) . We show that if \(n\ge 3\) and \(u\in C^{2}(\mathbb {B}^{n},{\mathbb R}^n) \cap C(\overline{\mathbb {B}^{n}},{\mathbb R}^n )\) is a solution to the hyperbolic Poisson equation, then it has the representation \(u=P_{h}[\phi ]-G_{ h}[\psi ]\) provided that \(u\mid _{\mathbb {S}^{n-1}}=\phi \) and \(\int _{\mathbb {B}^{n}}(1- x ^{2})^{n-1} \psi (x) \,d\tau (x)<\infty \) . Here \(P_{h}\) and \(G_{h}\) denote Poisson and Green integrals with respect to \(\Delta _{h}\) , respectively. Furthermore, we prove that functions of the form \(u=P_{h}[\phi ]-G_{h}[\psi ]\) are Lipschitz continuous.
      PubDate: 2017-12-21
      DOI: 10.1007/s00526-017-1290-x
      Issue No: Vol. 57, No. 1 (2017)
       
  • Regularity of harmonic maps from polyhedra to CAT(1) spaces
    • Authors: Christine Breiner; Ailana Fraser; Lan-Hsuan Huang; Chikako Mese; Pam Sargent; Yingying Zhang
      Abstract: We determine regularity results for energy minimizing maps from an n-dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the \((n-2)\) -skeleton, we improve the regularity to locally Lipschitz. Finally, for points \(x \in X^{(k)}\) with \(k \le n-2\) , we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of \(x \in X\) .
      PubDate: 2017-12-21
      DOI: 10.1007/s00526-017-1279-5
      Issue No: Vol. 57, No. 1 (2017)
       
  • On the Hölder continuous subsolution problem for the complex
           Monge–Ampère equation
    • Authors: Ngoc Cuong Nguyen
      Abstract: We give a necessary and sufficient condition for positive Borel measures such that the Dirichlet problem, with zero boundary data, for the complex Monge–Ampère equation admits Hölder continuous plurisubharmonic solutions. In particular, when the subsolution has finite Monge–Ampère total mass, we obtain an affirmative answer to a question of Zeriahi et al. (Complex Var. Elliptic Equ. 61(7):902–930, 2016).
      PubDate: 2017-12-20
      DOI: 10.1007/s00526-017-1297-3
      Issue No: Vol. 57, No. 1 (2017)
       
 
 
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
 
Home (Search)
Subjects A-Z
Publishers A-Z
Customise
APIs
Your IP address: 54.159.30.26
 
About JournalTOCs
API
Help
News (blog, publications)
JournalTOCs on Twitter   JournalTOCs on Facebook

JournalTOCs © 2009-