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MATHEMATICS (642 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: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
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: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
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: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
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: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
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: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
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: 4)
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: 8)
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: 6)
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: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
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 Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
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: 17)
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: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
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: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 6)
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: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
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: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
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: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
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: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
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: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
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: 3)
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: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        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  [2340 journals]
  • On Lipschitz solutions for some forward–backward parabolic equations.
           II: the case against Fourier
    • Authors: Seonghak Kim; Baisheng Yan
      Abstract: Abstract As a sequel to the paper Kim and Yan (Ann Inst H Poincaré Anal Non Linéaire. doi:10.1016/j.anihpc.2017.03.001, 2017), we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward–backward diffusion equations with diffusion fluxes violating Fourier’s inequality.
      PubDate: 2017-04-26
      DOI: 10.1007/s00526-017-1155-3
      Issue No: Vol. 56, No. 3 (2017)
  • Volume-preserving mean curvature flow for tubes in rank one symmetric
           spaces of non-compact type
    • Authors: Naoyuki Koike
      Abstract: Abstract First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space under certain condition for the radius function. Next, we prove that the tubeness is preserved along the flow in the case where the ambient space is a rank one symmetric space of non-compact type, the reflective submanifold is an invariant submanifold and the radius function of the initial tube is radial. Furthermore, in this case, we prove that the flow reaches to the invariant submanifold or it exists in infinite time and converges to another tube of constant mean curvature in the \(C^{\infty }\) -topology in infinite time.
      PubDate: 2017-04-25
      DOI: 10.1007/s00526-017-1156-2
      Issue No: Vol. 56, No. 3 (2017)
  • Periodic orbits of Gross–Pitaevskii in the disc with vortices
           following point vortex flow
    • Authors: Raghavendra Venkatraman
      Abstract: Abstract We prove the existence of non-constant time periodic vortex solutions to the Gross–Pitaevskii equations for small but fixed \(\varepsilon > 0.\) The vortices of these solutions follow periodic orbits to the point vortex system of ordinary differential equations for all time. The construction uses two approaches—constrained minimization techniques adapted from Gelantalis and Sternberg (J Math Phys 53:083701, 2012) and topological minimax techniques adapted from Lin and Lin (Sel Math New Ser 3:99–113, 1997), applied to a formulation of the problem within a rotational ansatz.
      PubDate: 2017-04-25
      DOI: 10.1007/s00526-017-1168-y
      Issue No: Vol. 56, No. 3 (2017)
  • Multiplicity and ellipticity of closed characteristics on compact
           star-shaped hypersurfaces in $$\mathbf{R}^{2n}$$ R 2 n
    • Authors: Huagui Duan; Hui Liu
      Abstract: Abstract In this paper, we firstly generalize some theories developed by Ekeland and Hofer (Commun Math Phys 113:419–467, 1987) for closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\) to star-shaped hypersurfaces. As applications we use Ekeland–Hofer theory and index iteration theory to prove that if a compact star-shaped hypersuface in \(\mathbf{R}^4\) satisfying some suitable pinching condition carries exactly two geometrically distinct closed characteristics, then both of them must be elliptic. We also conclude that the theory developed by Long and Zhu (Ann Math 155:317–368, 2002) still holds for dynamically convex star-shaped hypersurfaces, and combining it with the results in Wang et al. (Duke Math J 139:411–462, 2007), Liu et al. (J Funct Anal 266:5598–5638, 2014) and Wang (Adv Math 297:93–148, 2016), we obtain that there exist at least n closed characteristics on every dynamically convex star-shaped hypersurface in \(\mathbf{R}^{2n}\) for \(n=3, 4\) .
      PubDate: 2017-04-25
      DOI: 10.1007/s00526-017-1173-1
      Issue No: Vol. 56, No. 3 (2017)
  • Multiple solutions for resonant problems of the Robin p -Laplacian plus an
           indefinite potential
    • Authors: Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Dušan D. Repovš
      Abstract: Abstract We study a nonlinear boundary value problem driven by the p-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carathéodory function which is asymptotically resonant at \(\pm \infty \) with respect to a nonprincipal Ljusternik–Schnirelmann eigenvalue. Using variational methods, together with Morse theory and truncation-perturbation techniques, we show that the problem has at least three nontrivial smooth solutions, two of which have a fixed sign.
      PubDate: 2017-04-25
      DOI: 10.1007/s00526-017-1164-2
      Issue No: Vol. 56, No. 3 (2017)
  • Fisher–KPP equation with free boundaries and time-periodic
    • Authors: Ningkui Sun; Bendong Lou; Maolin Zhou
      Abstract: Abstract We consider a reaction–diffusion–advection equation of the form: \(u_t=u_{xx}-\beta (t)u_x+f(t,u)\) for \(x\in (g(t),h(t))\) , where \(\beta (t)\) is a T-periodic function representing the intensity of the advection, f(t, u) is a Fisher–KPP type of nonlinearity, T-periodic in t, g(t) and h(t) are two free boundaries satisfying Stefan conditions. This equation can be used to describe the population dynamics in time-periodic environment with advection. Its homogeneous version (that is, both \(\beta \) and f are independent of t) was recently studied by Gu et al. (J Funct Anal 269:1714–1768, 2015). In this paper we consider the time-periodic case and study the long time behavior of the solutions. We show that a vanishing–spreading dichotomy result holds when \(\beta \) is small; a vanishing–transition–virtual spreading trichotomy result holds when \(\beta \) is a medium-sized function; all solutions vanish when \(\beta \) is large. Here the partition of \(\beta (t)\) depends not only on the “size” \(\bar{\beta }:= \frac{1}{T}\int _0^T \beta (t) dt\) of \(\beta (t)\) but also on its “shape” \(\tilde{\beta }(t) := \beta (t) - \bar{\beta }\) .
      PubDate: 2017-04-24
      DOI: 10.1007/s00526-017-1165-1
      Issue No: Vol. 56, No. 3 (2017)
  • Compactness results for static and dynamic chiral skyrmions near the
           conformal limit
    • Authors: Lukas Döring; Christof Melcher
      Abstract: Abstract We examine lower order perturbations of the harmonic map problem from \(\mathbb {R}^2\) to \(\mathbb {S}^2\) including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform background state. Energy functionals of this type arise in the context of magnetic systems without inversion symmetry. In the almost conformal regime, where these perturbations are weighted with a small parameter, we examine the existence of relative minimizers in a non-trivial homotopy class, so-called chiral skyrmions, strong compactness of almost minimizers, and their asymptotic limit. Finally we examine dynamic stability and compactness of almost minimizers in the context of the Landau–Lifshitz–Gilbert equation including spin-transfer torques arising from the interaction with an external current.
      PubDate: 2017-04-24
      DOI: 10.1007/s00526-017-1172-2
      Issue No: Vol. 56, No. 3 (2017)
  • On inverse mean curvature flow in Schwarzschild space and Kottler space
    • Authors: Haizhong Li; Yong Wei
      Abstract: Abstract In this paper, we first study the behavior of inverse mean curvature flow in Schwarzschild manifold. We show that if the initial hypersurface \(\Sigma \) is strictly mean convex and star-shaped, then the flow hypersurface \(\Sigma _t\) converges to a large coordinate sphere as \(t\rightarrow \infty \) exponentially. We also describe an application of this convergence result. In the second part of this paper, we will analyse the inverse mean curvature flow in Kottler–Schwarzschild manifold. By deriving a lower bound for the mean curvature on the flow hypersurface independently of the initial mean curvature, we can use an approximation argument to show the global existence and regularity of the smooth inverse mean curvature flow for star-shaped and weakly mean convex initial hypersurface, which generalizes Huisken–Ilmanen’s (J Differ Geom 80:433–451, 2008) result.
      PubDate: 2017-04-24
      DOI: 10.1007/s00526-017-1160-6
      Issue No: Vol. 56, No. 3 (2017)
  • On the simultaneous homogenization and dimension reduction in elasticity
           and locality of $$\varGamma $$ Γ -closure
    • Authors: Mario Bukal; Igor Velčić
      Abstract: Abstract We provide a framework for simultaneous homogenization and dimension reduction in the setting of linearized elasticity as well as non-linear elasticity for the derivation of homogenized von Kármán plate and bending rod models. The framework encompasses even perforated domains and domains with oscillatory boundary, provided that the corresponding extension operator can be constructed. Locality property of \(\varGamma \) -closure is established, i.e. every energy density obtained by the homogenization process can be in almost every point obtained as the limit of periodic energy densities.
      PubDate: 2017-04-24
      DOI: 10.1007/s00526-017-1167-z
      Issue No: Vol. 56, No. 3 (2017)
  • Existence of multiple periodic solutions to asymptotically linear wave
           equations in a ball
    • Authors: Jianyi Chen; Zhitao Zhang
      Abstract: Abstract This paper is concerned with the Dirichlet problem of the asymptotically linear wave equation $$\begin{aligned} u_{tt}-\Delta u = g(t,x,u) \end{aligned}$$ in a n-dimensional ball with radius R, where \(n>1\) and g(t, x, u) is radially symmetric in x and T-periodic in time. An interesting feature is that the solvable of the problem depends on the space dimension n and the arithmetical properties of R and T. Based on the spectral properties of the radially symmetric wave operator, we use the saddle point reduction and variational methods to construct at least three radially symmetric solutions with time period T, when T is a rational multiple of R and g(t, x, u) satisfies some monotonicity and asymptotically linear conditions.
      PubDate: 2017-04-22
      DOI: 10.1007/s00526-017-1154-4
      Issue No: Vol. 56, No. 3 (2017)
  • Erratum to: Multiple solutions to logarithmic Schrödinger equations
           with periodic potential
    • Authors: Marco Squassina; Andrzej Szulkin
      PubDate: 2017-04-13
      DOI: 10.1007/s00526-017-1127-7
      Issue No: Vol. 56, No. 3 (2017)
  • Variations, approximation, and low regularity in one dimension
    • Authors: Richard Gratwick
      Abstract: Abstract We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general of the form of a standard Lipschitz “variation”. Part of this investigation, but of interest in its own right, is an example of a nowhere locally Lipschitz minimizer which serves as a counter-example to any putative Tonelli partial regularity statement. Under these low assumptions we find it nonetheless remains possible to derive necessary conditions for minimizers, in terms of approximate continuity and equality of the one-sided derivatives.
      PubDate: 2017-04-13
      DOI: 10.1007/s00526-017-1135-7
      Issue No: Vol. 56, No. 3 (2017)
  • Uniaxial versus biaxial character of nematic equilibria in three
    • Authors: Duvan Henao; Apala Majumdar; Adriano Pisante
      Abstract: Abstract We study global minimizers of the Landau–de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are specific to an asymptotic limit coined in terms of a dimensionless temperature and material-dependent parameter, t and some constraints on the material parameters, and we work in the \(t\rightarrow \infty \) limit that captures features of the widely used Lyuksyutov constraint (Kralj and Virga in J Phys A 34:829–838, 2001). We prove (i) that (re-scaled) global LdG minimizers converge uniformly to a (minimizing) limiting harmonic map, away from the singular set of the limiting map; (ii) we have points of maximal biaxiality and uniaxiality near each singular point of the limiting map; (iii) estimates for the size of “strongly biaxial” regions in terms of the parameter t. We further show that global LdG minimizers in the restricted class of uniaxial \(\mathbf{Q}\) -tensors cannot be stable critical points of the LdG energy in this limit.
      PubDate: 2017-04-04
      DOI: 10.1007/s00526-017-1142-8
      Issue No: Vol. 56, No. 2 (2017)
  • Condensation of fermion pairs in a domain
    • Authors: Rupert L. Frank; Marius Lemm; Barry Simon
      Abstract: Abstract We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two-body potential which admits a bound state. The particles are confined to a domain with Dirichlet boundary conditions. Starting from the microscopic BCS theory, we derive an effective macroscopic Gross–Pitaevskii (GP) theory describing the condensate of fermion pairs. The GP theory also has Dirichlet boundary conditions. Along the way, we prove that the GP energy, defined with Dirichlet boundary conditions on a bounded Lipschitz domain, is continuous under interior and exterior approximations of that domain.
      PubDate: 2017-04-03
      DOI: 10.1007/s00526-017-1140-x
      Issue No: Vol. 56, No. 2 (2017)
  • Isoperimetry with upper mean curvature bounds and sharp stability
    • Authors: B. Krummel; F. Maggi
      Abstract: Abstract It was proved by Almgren that among boundaries whose mean curvature is bounded from above, perimeter is uniquely minimized by balls. We obtain sharp stability estimates for Almgren’s isoperimetric principle and, as an application, we deduce a sharp description of boundaries with almost constant mean curvature under a total perimeter bound which prevents bubbling.
      PubDate: 2017-03-24
      DOI: 10.1007/s00526-017-1139-3
      Issue No: Vol. 56, No. 2 (2017)
  • Infinitely many non-radial solutions for fractional Nirenberg problem
    • Authors: Chungen Liu; Qiang Ren
      Abstract: Abstract In this paper, the prescribed \(\sigma \) -curvature problem $$\begin{aligned} P_{\sigma }^{g_0} u={\tilde{K}}(x)u^{\frac{N+2\sigma }{N-2\sigma }}, x\in {\mathbb {S}}^N,u>0 \end{aligned}$$ is considered. When \({\tilde{K}}(x)\) is some axis symmetric function on \({\mathbb {S}}^N\) , by using singular perturbation method, it is proved that this problem possesses infinitely many non-radial solutions for \(0<\sigma \le 1\) and \(N> 2\sigma +2\) .
      PubDate: 2017-03-23
      DOI: 10.1007/s00526-017-1141-9
      Issue No: Vol. 56, No. 2 (2017)
  • Discreteness of interior transmission eigenvalues revisited
    • Authors: Hoai-Minh Nguyen; Quoc-Hung Nguyen
      Abstract: Abstract This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.
      PubDate: 2017-03-22
      DOI: 10.1007/s00526-017-1143-7
      Issue No: Vol. 56, No. 2 (2017)
  • Regularity of $$\omega $$ ω -minimizers for a class of functionals with
           non-standard growth
    • Authors: Jihoon Ok
      Abstract: Abstract We prove local Hölder continuity results for \(\omega \) -minimizers of a class of functionals with non-standard growth, characterized by the fact of having a double type of degeneracy, and thereby extending to \(\omega \) -minimizers the results obtained in Colombo and Mingione (Arch Ration Mech Anal 215(2):443–496, 2015) for ordinary minimizers. As a side benefit of the proof, we also consider a class of functionals with Orlicz-growth and prove regularity for \(\omega \) -minimizers.
      PubDate: 2017-03-21
      DOI: 10.1007/s00526-017-1137-5
      Issue No: Vol. 56, No. 2 (2017)
  • On the p -Laplacian with Robin boundary conditions and boundary trace
    • Authors: Hynek Kovařík; Konstantin Pankrashkin
      Abstract: Abstract Let \(\Omega \subset \mathbb {R}^\nu \) , \(\nu \ge 2\) , be a \(C^{1,1}\) domain whose boundary \(\partial \Omega \) is either compact or behaves suitably at infinity. For \(p\in (1,\infty )\) and \(\alpha >0\) , define $$\begin{aligned} \Lambda (\Omega ,p,\alpha ):=\inf _{\begin{array}{c} u\in W^{1,p}(\Omega )\\ u\not \equiv 0 \end{array}}\dfrac{\displaystyle \int _\Omega \nabla u ^p \mathrm {d} x - \alpha \displaystyle \int _{\partial \Omega } u ^p\mathrm {d}\sigma }{\displaystyle \int _\Omega u ^p\mathrm {d} x}, \end{aligned}$$ where \(\mathrm {d}\sigma \) is the surface measure on \(\partial \Omega \) . We show the asymptotics $$\begin{aligned} \Lambda (\Omega ,p,\alpha )=-(p-1)\alpha ^{\frac{p}{p-1}} - (\nu -1)H_\mathrm {max}\, \alpha + o(\alpha ), \quad \alpha \rightarrow +\infty , \end{aligned}$$ where \(H_\mathrm {max}\) is the maximum mean curvature of \(\partial \Omega \) . The asymptotic behavior of the associated minimizers is discussed as well. The estimate is then applied to the study of the best constant in a boundary trace theorem for expanding domains, to the norm estimate for extension operators and to related isoperimetric inequalities.
      PubDate: 2017-03-21
      DOI: 10.1007/s00526-017-1138-4
      Issue No: Vol. 56, No. 2 (2017)
  • Estimates for the first eigenvalue of Jacobi operator on hypersurfaces
           with constant mean curvature in spheres
    • Authors: Daguang Chen; Qing-Ming Cheng
      Abstract: Abstract In this paper, we study the first eigenvalue of Jacobi operator on an n-dimensional non-totally umbilical compact hypersurface with constant mean curvature H in the unit sphere \(S^{n+1}(1)\) . We give an optimal upper bound for the first eigenvalue of Jacobi operator, which only depends on the mean curvature H and the dimension n. This bound is attained if and only if, \(\varphi :\ M \rightarrow S^{n+1}(1)\) is isometric to \(S^1(r)\times S^{n-1}(\sqrt{1-r^2})\) when \(H\ne 0\) or \(\varphi :\ M \rightarrow S^{n+1}(1)\) is isometric to a Clifford torus \( S^{n-k}\left( \sqrt{\dfrac{n-k}{n}}\right) \times S^k\left( \sqrt{\dfrac{k}{n}}\right) \) , for \(k=1, 2, \ldots , n-1\) when \(H=0\) .
      PubDate: 2017-03-21
      DOI: 10.1007/s00526-017-1132-x
      Issue No: Vol. 56, No. 2 (2017)
School of Mathematical and Computer Sciences
Heriot-Watt University
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