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MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
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: 8)
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: 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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
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: 10)
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: 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: 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: 3)
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: 10)
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: 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: 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 Network Science     Open Access  
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: 19)
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: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
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: 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: 2)
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: 14)
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: 29)
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: 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: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
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)

        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]
  • A minimal partition problem with trace constraint in the Grushin plane
    • Authors: Valentina Franceschi
      Abstract: We study a variational problem for the perimeter associated with the Grushin plane, called minimal partition problem with trace constraint. This consists in studying how to enclose three prescribed areas in the Grushin plane, using the least amount of perimeter, under an additional “one-dimensional” constraint on the intersections of their boundaries. We prove existence of regular solutions for this problem, and we characterize them in terms of isoperimetric sets, showing differences with the Euclidean case. The problem arises from the study of quantitative isoperimetric inequalities and has connections with the theory of minimal clusters.
      PubDate: 2017-07-08
      DOI: 10.1007/s00526-017-1198-5
      Issue No: Vol. 56, No. 4 (2017)
  • An iterative method for generated Jacobian equations
    • Authors: Farhan Abedin; Cristian E. Gutiérrez
      Abstract: The purpose of this paper is to present an iterative scheme to find approximate solutions, to any preset degree of accuracy, for a class of generated Jacobian equations introduced in Trudinger (Discrete Contin Dyn Syst 34(4): 1663–1681 2014). A proof of an upper bound on the number of iteration steps, without assuming any condition of Ma-Trudinger-Wang type, is presented. Applications to optimal mass transport and to the parallel reflector problem in optics are also provided.
      PubDate: 2017-07-07
      DOI: 10.1007/s00526-017-1200-2
      Issue No: Vol. 56, No. 4 (2017)
  • Variational approach to coarse-graining of generalized gradient flows
    • Authors: Manh Hong Duong; Agnes Lamacz; Mark A. Peletier; Upanshu Sharma
      Abstract: In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (a) a natural interaction between the duality structure and the coarse-graining, (b) application to systems with non-dissipative effects, and (c) application to coarse-graining of approximate solutions which solve the equation only to some error. As examples, we use this technique to solve three limit problems, the overdamped limit of the Vlasov–Fokker–Planck equation and the small-noise limit of randomly perturbed Hamiltonian systems with one and with many degrees of freedom.
      PubDate: 2017-06-28
      DOI: 10.1007/s00526-017-1186-9
      Issue No: Vol. 56, No. 4 (2017)
  • Symmetry, quantitative Liouville theorems and analysis of large solutions
           of conformally invariant fully nonlinear elliptic equations
    • Authors: YanYan Li; Luc Nguyen
      Abstract: We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem.
      PubDate: 2017-06-19
      DOI: 10.1007/s00526-017-1192-y
      Issue No: Vol. 56, No. 4 (2017)
  • On locally conformally flat manifolds with finite total Q -curvature
    • Authors: Zhiqin Lu; Yi Wang
      Abstract: In this paper, we study the ends of a locally conformally flat complete manifold with finite total Q-curvature. We prove that for such a manifold, the integral of the Q-curvature equals an integral multiple of a dimensional constant \(c_n\) , where \(c_n\) is the integral of the Q-curvature on the unit n-sphere. It provides further evidence that the Q-curvature on a locally conformally flat manifold controls geometry as the Gaussian curvature does in two dimension.
      PubDate: 2017-06-16
      DOI: 10.1007/s00526-017-1189-6
      Issue No: Vol. 56, No. 4 (2017)
  • Asymptotic behaviors of Landau–Lifshitz flows from $$\mathbb {R}^2$$ R 2
           to Kähler manifolds
    • Authors: Ze Li; Lifeng Zhao
      Abstract: In this paper, we study the asymptotic behaviors of finite energy solutions to the Landau–Lifshitz flows from \(\mathbb {R}^2\) into Kähler manifolds. First, we prove that the solution with initial data below the critical energy converges to a constant map in the energy space as \(t\rightarrow \infty \) for the compact Riemannian surface targets. In particular, when the target is a two dimensional sphere, we prove that the solution to the Landau–Lifshitz–Gilbert equation with initial data having an energy below \(4\pi \) converges to some constant map in the energy space. The proof bases on the method of induction on energy and geometric renormalizations. Second, for general compact Kähler manifolds and initial data of an arbitrary finite energy, we obtain a bubbling theorem analogous to the Struwe’s results on the heat flows.
      PubDate: 2017-06-10
      DOI: 10.1007/s00526-017-1182-0
      Issue No: Vol. 56, No. 4 (2017)
  • A natural approach to the asymptotic mean value property for the p
    • Authors: Michinori Ishiwata; Rolando Magnanini; Hidemitsu Wadade
      Abstract: Let \(1\le p\le \infty \) . We show that a function \(u\in C(\mathbb R^N)\) is a viscosity solution to the normalized p-Laplace equation \(\Delta _p^n u(x)=0\) if and only if the asymptotic formula $$\begin{aligned} u(x)=\mu _p(\varepsilon ,u)(x)+o(\varepsilon ^2) \end{aligned}$$ holds as \(\varepsilon \rightarrow 0\) in the viscosity sense. Here, \(\mu _p(\varepsilon ,u)(x)\) is the p-mean value of u on \(B_\varepsilon (x)\) characterized as a unique minimizer of $$\begin{aligned} \Vert u-\lambda \Vert _{L^p(B_\varepsilon (x))} \end{aligned}$$ with respect to \(\lambda \in {\mathbb {R}}\) . This kind of asymptotic mean value property (AMVP) extends to the case \(p=1\) previous (AMVP)’s obtained when \(\mu _p(\varepsilon ,u)(x)\) is replaced by other kinds of mean values. The natural definition of \(\mu _p(\varepsilon ,u)(x)\) makes sure that this is a monotonic and continuous (in the appropriate topology) functional of u. These two properties help to establish a fairly general proof of (AMVP), that can also be extended to the (normalized) parabolic p-Laplace equation.
      PubDate: 2017-06-10
      DOI: 10.1007/s00526-017-1188-7
      Issue No: Vol. 56, No. 4 (2017)
  • Homogenization of viscous and non-viscous HJ equations: a remark and an
    • Authors: Andrea Davini; Elena Kosygina
      Abstract: It was pointed out by P.-L. Lions, G. Papanicolaou, and S.R.S. Varadhan in their seminal paper (1987) that, for first order Hamilton–Jacobi (HJ) equations, homogenization starting with affine initial data implies homogenization for general uniformly continuous initial data. The argument makes use of some properties of the HJ semi-group, in particular, the finite speed of propagation. This property is lost for viscous HJ equations. In this paper we prove the above mentioned implication in both viscous and non-viscous cases. Our proof relies on a variant of Evans’s perturbed test function method. As an application, we show homogenization in the stationary ergodic setting for viscous and non-viscous HJ equations in one space dimension with non-convex Hamiltonians of specific form. The results are new in the viscous case.
      PubDate: 2017-06-08
      DOI: 10.1007/s00526-017-1177-x
      Issue No: Vol. 56, No. 4 (2017)
  • The Moser–Trudinger inequality and its extremals on a disk via
           energy estimates
    • Authors: Gabriele Mancini; Luca Martinazzi
      Abstract: We study the Dirichlet energy of non-negative radially symmetric critical points \(u_\mu \) of the Moser–Trudinger inequality on the unit disc in \(\mathbb {R}^2\) , and prove that it expands as $$\begin{aligned} 4\pi +\frac{4\pi }{\mu ^{4}}+o(\mu ^{-4})\le \int _{B_1} \nabla u_\mu ^2dx\le 4\pi +\frac{6\pi }{\mu ^{4}}+o(\mu ^{-4}),\quad \text {as }\mu \rightarrow \infty , \end{aligned}$$ where \(\mu =u_\mu (0)\) is the maximum of \(u_\mu \) . As a consequence, we obtain a new proof of the Moser–Trudinger inequality, of the Carleson–Chang result about the existence of extremals, and of the Struwe and Lamm–Robert–Struwe multiplicity result in the supercritical regime (only in the case of the unit disk). Our results are stable under sufficiently weak perturbations of the Moser–Trudinger functional. We explicitly identify the critical level of perturbation for which, although the perturbed Moser–Trudinger inequality still holds, the energy of its critical points converges to \(4\pi \) from below. We expect, in some of these cases, that the existence of extremals does not hold, nor the existence of critical points in the supercritical regime.
      PubDate: 2017-06-08
      DOI: 10.1007/s00526-017-1184-y
      Issue No: Vol. 56, No. 4 (2017)
  • Theory of light-matter interaction in nematic liquid crystals and the
           second Painlevé equation
    • Authors: Marcel G. Clerc; Juan Diego Dávila; Michał Kowalczyk; Panayotis Smyrnelis; Estefania Vidal-Henriquez
      Abstract: We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow kink. Its local profile is described by the generalized Hastings and McLeod solutions of the second Painlevé equation (Claeys et al. in Ann Math 168(2):601–641, 2008; Hastings and McLeod in Arch Ration Mech Anal 73(1):31–51, 1980). As part of our analysis we give a new proof of existence of these solutions.
      PubDate: 2017-06-07
      DOI: 10.1007/s00526-017-1187-8
      Issue No: Vol. 56, No. 4 (2017)
  • Two solutions for an elliptic problem with two singular terms
    • Authors: Giovanni Anello; Francesca Faraci
      Abstract: We study the Dirichlet boundary value problem with 0-boundary data for the semilinear elliptic equation \(-\Delta u= (\lambda u^{s-1}-u^{r-1})\chi _{\{u>0\}}\) in a bounded domain \(\Omega \) , where \(0<r<s<1\) and \(\lambda \in (0,\infty )\) . In particular, for \(\lambda \) large enough, we prove the existence of at least two nonnegative solutions, one of which is positive, satisfies the Hopf’s boundary condition and corresponds to a local minimum of the energy functional. This paper is motivated by a recent result of the authors where the same conclusion was obtained for the case \(0<r\le 1< s<2\) .
      PubDate: 2017-06-06
      DOI: 10.1007/s00526-017-1179-8
      Issue No: Vol. 56, No. 4 (2017)
  • Variational methods for the selection of solutions to an implicit system
           of PDE
    • Authors: Gisella Croce; Giovanni Pisante
      Abstract: We consider the vectorial system $$\begin{aligned} {\left\{ \begin{array}{ll} Du \in \mathcal {O}(2), &{} \text{ a.e. } \text{ in }\,\;\Omega , \\ u=0, &{} \text{ on } \,\;\partial \Omega , \end{array}\right. } \end{aligned}$$ where \(\Omega \) is a subset of \(\mathbb R^2\) , \(u:\Omega \rightarrow \mathbb R^2\) and \(\mathcal {O}(2)\) is the orthogonal group of \(\mathbb R^2\) . We provide a variational method to select, among the infinitely many solutions, the ones that minimize an appropriate weighted measure of some set of singularities of the gradient.
      PubDate: 2017-06-06
      DOI: 10.1007/s00526-017-1185-x
      Issue No: Vol. 56, No. 4 (2017)
  • Uniform regularity and convergence of phase-fields for Willmore’s
    • Authors: Patrick W. Dondl; Stephan Wojtowytsch
      Abstract: We investigate the convergence of phase fields for the Willmore problem away from the support of a limiting measure \(\mu \) . For this purpose, we introduce a suitable notion of essentially uniform convergence. This mode of convergence is a natural generalisation of uniform convergence that precisely describes the convergence of phase fields in three dimensions. More in detail, we show that, in three space dimensions, points close to which the phase fields stay bounded away from a pure phase lie either in the support of the limiting mass measure \(\mu \) or contribute a positive amount to the limiting Willmore energy. Thus there can only be finitely many such points. As an application, we investigate the Hausdorff limit of level sets of sequences of phase fields with bounded energy. We also obtain results on boundedness and \(L^p\) -convergence of phase fields and convergence from outside the interval between the wells of a double-well potential. For minimisers of suitable energy functionals, we deduce uniform convergence of the phase fields from essentially uniform convergence.
      PubDate: 2017-06-05
      DOI: 10.1007/s00526-017-1178-9
      Issue No: Vol. 56, No. 4 (2017)
  • Concavity of the Lagrangian phase operator and applications
    • Authors: Tristan C. Collins; Sebastien Picard; Xuan Wu
      Abstract: We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if \(\Omega \) is a compact domain in \({\mathbb {R}}^{n}\) or \({\mathbb {C}}^n\) , then there exists a solution to the Dirichlet problem with right-hand side h(x) satisfying \( h(x) > (n-2)\frac{\pi }{2}\) and boundary data \(\varphi \) if and only if there exists a subsolution.
      PubDate: 2017-06-05
      DOI: 10.1007/s00526-017-1191-z
      Issue No: Vol. 56, No. 4 (2017)
  • Asymmetric ( p , 2)-equations with double resonance
    • Authors: Leszek Gasiński; Nikolaos S. Papageorgiou
      Abstract: We consider a nonlinear Dirichlet elliptic problem driven by the sum of a p-Laplacian and a Laplacian [a (p, 2)-equation] and with a reaction term, which is superlinear in the positive direction (without satisfying the Ambrosetti–Rabinowitz condition) and sublinear resonant in the negative direction. Resonance can also occur asymptotically at zero. So, we have a double resonance situation. Using variational methods based on the critical point theory and Morse theory (critical groups), we establish the existence of at least three nontrivial smooth solutions.
      PubDate: 2017-06-03
      DOI: 10.1007/s00526-017-1180-2
      Issue No: Vol. 56, No. 3 (2017)
  • Uniqueness results on surfaces with boundary
    • Authors: Xiaodong Wang
      PubDate: 2017-06-02
      DOI: 10.1007/s00526-017-1190-0
      Issue No: Vol. 56, No. 3 (2017)
  • On Willmore Legendrian surfaces in $$\mathbb {S}^5$$ S 5 and the contact
           stationary Legendrian Willmore surfaces
    • Authors: Yong Luo
      Abstract: In this paper we study Willmore Legendrian surfaces (that is Legendrian surfaces which are critical points of the Willmore functional). We use an equality proved in Luo (arXiv:1211.4227v6) to get a relation between Willmore Legendrian surfaces and contact stationary Legendrian surfaces in \(\mathbb {S}^5\) , and then we use this relation to prove a classification result for Willmore Legendrian spheres in \(\mathbb {S}^5\) . We also get an integral inequality for Willmore Legendrian surfaces and in particular we prove that if the square length of the second fundamental form of a Willmore Legendrian surface in \(\mathbb {S}^5\) belongs to [0, 2], then it must be 0 and L is totally geodesic or 2 and L is a flat minimal Legendrian tori, which generalizes the result of Yamaguchi et al. (Proc Am Math Soc 54:276–280, 1976). We also study variation of the Willmore functional among Legendrian surfaces in 5-dimensional Sasakian manifolds. Let \(\Sigma \) be a closed surface and \((M,\alpha ,g_\alpha ,J)\) a 5-dimensional Sasakian manifold with a contact form \(\alpha \) , an associated metric \(g_\alpha \) and an almost complex structure J. Assume that \(f:\Sigma \mapsto M\) is a Legendrian immersion. Then f is called a contact stationary Legendrian Willmore surface (in short, a csL Willmore surface) if it is a critical point of the Willmore functional under contact deformations. To investigate the existence of csL Willmore surfaces we introduce a higher order flow which preserves the Legendre condition and decreases the Willmore energy. As a first step we prove that this flow is well posed if \((M,\alpha ,g_\alpha ,J)\) is a Sasakian Einstein manifold, in particular \(\mathbb {S}^5\) .
      PubDate: 2017-06-02
      DOI: 10.1007/s00526-017-1183-z
      Issue No: Vol. 56, No. 3 (2017)
  • Domain variations and moving boundary problems
    • Authors: Patrick Guidotti
      Abstract: In the past few decades maximal regularity theory has successfully been applied to moving boundary problems. The basic idea is to reduce the system with varying domains to one in a fixed domain. This is done by a transformation, the so-called Hanzawa transformation, and yields a typically nonlocal and nonlinear coupled system of (evolution) equations. Well-posedness results can then often be established as soon as it is proved that the relevant linearization is the generator of an analytic semigroup or admits maximal regularity. To implement this program, it is necessary to somehow parametrize to space of boundaries/domains (typically the space of compact hypersurfaces \(\Gamma \) in \({\mathbb {R}}^n\) , in the Euclidean setting). This has traditionally been achieved by means of the already mentioned Hanzawa transformation. The approach, while successful, requires the introduction of a smooth manifold \(\Gamma _\infty \) close to the manifold \(\Gamma _0\) in which one cares to linearize. This prevents one to use coordinates in which \(\Gamma _0\) lies at their “center”. As a result formulæ tend to contain terms that would otherwise not be present were one able to linearize in a neighborhood emanating from \(\Gamma _0\) instead of from \(\Gamma _\infty \) . In this paper it is made use of flows (curves of diffeomorphisms) to obtain a general form of the relevant linearization in combination with an alternative coordinatization of the manifold of hypersurfaces, which circumvents the need for the introduction of a “phantom” reference manifold \(\Gamma _\infty \) by, in its place, making use of a “phantom geometry” on \(\Gamma _0\) . The upshot is a clear insight into the structure of the linearization, simplified calculations, and simpler formulæ for the resulting linear operators, which are useful in applications.
      PubDate: 2017-06-02
      DOI: 10.1007/s00526-017-1181-1
      Issue No: Vol. 56, No. 3 (2017)
  • The deformation of symplectic critical surfaces in a Kähler
    • Authors: Xiaoli Han; Jiayu Li; Jun Sun
      Abstract: In this paper we consider the compactness of \(\beta \) -symplectic critical surfaces in a Kähler surface. Let M be a compact Kähler surface and \(\Sigma _i\subset M\) be a sequence of closed \(\beta _i\) -symplectic critical surfaces with \(\beta _i\rightarrow \beta _0\in (0,\infty )\) . Suppose the quantity \(\int _{\Sigma _i}\frac{1}{\cos ^q\alpha _i}d\mu _i\) (for some \(q>4\) ) and the genus of \(\Sigma _{i}\) are bounded, then there exists a finite set of points \({{\mathcal {S}}}\subset M\) and a subsequence \(\Sigma _{i'}\) which converges uniformly in the \(C^l\) topology (for any \(l<\infty \) ) on compact subsets of \(M\backslash {{\mathcal {S}}}\) to a \(\beta _0\) -symplectic critical surface \(\Sigma \subset M\) , each connected component of \(\Sigma \setminus {{\mathcal {S}}}\) can be extended smoothly across \({{\mathcal {S}}}\) .
      PubDate: 2017-06-01
      DOI: 10.1007/s00526-017-1175-z
      Issue No: Vol. 56, No. 3 (2017)
  • Radial graphs of constant curvature and prescribed boundary
    • Authors: Flávio F. Cruz
      Abstract: In this paper we are concerned with the problem of finding hypersurfaces of constant curvature and prescribed boundary in the Euclidean space, without assuming the convexity of the prescribed solution and using the theory of fully nonlinear elliptic equations. If the given data admits a suitable radial graph as a subsolution, then we prove that there exists a radial graph with constant curvature and realizing the prescribed boundary. As an application, it is proved that if \(\Omega \subset \mathbb {S}^n\) is a mean convex domain whose closure is contained in an open hemisphere of \(\mathbb {S}^n\) then, for \(0<R<n(n-1),\) there exists a radial graph of constant scalar curvature R and boundary \(\partial \Omega \) .
      PubDate: 2017-05-31
      DOI: 10.1007/s00526-017-1176-y
      Issue No: Vol. 56, No. 3 (2017)
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