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MATHEMATICS (706 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: 15)
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: 27)
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: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 12)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
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: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
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: 6)
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: 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: 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: 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)
ANZIAM Journal     Open Access   (Followers: 1)
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: 11)
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: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
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: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
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   (Followers: 1)
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 Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (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: 18)
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: 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: 1)
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: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
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: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
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: 5)
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: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
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  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
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: 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)

        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  [2351 journals]
  • Periodic solutions for critical fractional problems
    • Authors: Vincenzo Ambrosio
      Abstract: We deal with the existence of \(2\pi \) -periodic solutions to the following non-local critical problem $$\begin{aligned} \left\{ \begin{array}{ll} [(-\Delta _{x}+m^{2})^{s}-m^{2s}]u=W(x) u ^{2^{*}_{s}-2}u+ f(x, u) &{}\quad \text{ in } \; (-\pi ,\pi )^{N} \\ u(x+2\pi e_{i})=u(x) &{}\quad \text{ for } \text{ all } \; x \in \mathbb {R}^{N}, \quad i=1, \dots , N, \end{array} \right. \end{aligned}$$ where \(s\in (0,1)\) , \(N \ge 4s\) , \(m\ge 0\) , \(2^{*}_{s}=\frac{2N}{N-2s}\) is the fractional critical Sobolev exponent, W(x) is a positive continuous function, and f(x, u) is a superlinear \(2\pi \) -periodic (in x) continuous function with subcritical growth. When \(m>0\) , the existence of a nonconstant periodic solution is obtained by applying the Linking Theorem, after transforming the above non-local problem into a degenerate elliptic problem in the half-cylinder \((-\,\pi ,\pi )^{N}\times (0, \infty )\) , with a nonlinear Neumann boundary condition, through a suitable variant of the extension method in periodic setting. We also consider the case \(m=0\) by using a careful procedure of limit. As far as we know, all these results are new.
      PubDate: 2018-02-22
      DOI: 10.1007/s00526-018-1317-y
      Issue No: Vol. 57, No. 2 (2018)
  • The conical complex Monge–Ampère equations on Kähler
    • Authors: Jiawei Liu; Chuanjing Zhang
      Abstract: In this paper, by providing the uniform gradient estimates for approximating equations, we prove the existence, uniqueness and regularity of conical parabolic complex Monge–Ampère equation with weak initial data. As an application, we obtain a regularity estimate, that is, any \(L^{\infty }\) -solution of the conical complex Monge–Ampère equation admits the \(C^{2,\alpha ,\beta }\) -regularity.
      PubDate: 2018-02-19
      DOI: 10.1007/s00526-018-1318-x
      Issue No: Vol. 57, No. 2 (2018)
  • Minimizers for the fractional Sobolev inequality on domains
    • Authors: Rupert L. Frank; Tianling Jin; Jingang Xiong
      Abstract: We consider a version of the fractional Sobolev inequality in domains and study whether the best constant in this inequality is attained. For the half-space and a large class of bounded domains we show that a minimizer exists, which is in contrast to the classical Sobolev inequalities in domains.
      PubDate: 2018-02-17
      DOI: 10.1007/s00526-018-1304-3
      Issue No: Vol. 57, No. 2 (2018)
  • Starshaped compact hypersurfaces with prescribed Weingarten curvature in
           warped product manifolds
    • Authors: Daguang Chen; Haizhong Li; Zhizhang Wang
      Abstract: Given a compact Riemannian manifold M, we consider a warped product manifold \({\bar{M}} = I \times _h M\) , where I is an open interval in \({\mathbb {R}}\) . For a positive function \(\psi \) defined on \({\bar{M}}\) , we generalize the arguments in Guan et al. (Commun. Pure Appl. Math. 68(8):1287–1325, 2015) and Ren and Wang (On the curvature estimates for Hessian equations, 2016. arXiv:1602.06535), to obtain the curvature estimates for Hessian equations \(\sigma _k(\kappa )=\psi (V,\nu (V))\) . We also obtain some existence results for the starshaped compact hypersurface \(\Sigma \) satisfying the above equation with various assumptions.
      PubDate: 2018-02-16
      DOI: 10.1007/s00526-018-1314-1
      Issue No: Vol. 57, No. 2 (2018)
  • Separable infinity harmonic functions in cones
    • Authors: Marie-Françoise Bidaut-Véron; Marta Garcia-Huidobro; Laurent Véron
      Abstract: We study the existence of separable infinity harmonic functions in any cone of \(\mathbb R^N\) vanishing on its boundary under the form \(u(r,\sigma )=r^{-\beta }\psi (\sigma )\) . We prove that such solutions exist, the spherical part \(\psi \) satisfies a nonlinear eigenvalue problem on a subdomain of the sphere \(S^{N-1}\) and that the exponents \(\beta =\beta _+>0\) and \(\beta =\beta _-<0\) are uniquely determined if the domain is smooth. We extend some of our results to non-smooth domains.
      PubDate: 2018-02-15
      DOI: 10.1007/s00526-018-1309-y
      Issue No: Vol. 57, No. 2 (2018)
  • The multiplier problem of the calculus of variations for scalar ordinary
           differential equations
    • Authors: Hardy Chan
      Abstract: In the long-standing inverse problem of the calculus of variations one is asked to find a Lagrangian and a multiplier so that a given differential equation, after being multiplied with the multiplier, becomes the Euler–Lagrange equation for the Lagrangian. An answer to this problem for the case of a scalar ordinary differential equation of order \(2n, n\ge 2,\) is proposed.
      PubDate: 2018-02-14
      DOI: 10.1007/s00526-018-1302-5
      Issue No: Vol. 57, No. 2 (2018)
  • Variational convergence of discrete geometrically-incompatible elastic
    • Authors: Raz Kupferman; Cy Maor
      Abstract: We derive a continuum model for incompatible elasticity as a variational limit of a family of discrete nearest-neighbor elastic models. The discrete models are based on discretizations of a smooth Riemannian manifold \(({\mathcal {M}},\mathfrak {g})\) , endowed with a flat, symmetric connection \(\nabla \) . The metric \(\mathfrak {g}\) determines local equilibrium distances between neighboring points; the connection \(\nabla \) induces a lattice structure shared by all the discrete models. The limit model satisfies a fundamental rigidity property: there are no stress-free configurations, unless \(\mathfrak {g}\) is flat, i.e., has zero Riemann curvature. Our analysis focuses on two-dimensional systems, however, all our results readily generalize to higher dimensions.
      PubDate: 2018-02-14
      DOI: 10.1007/s00526-018-1306-1
      Issue No: Vol. 57, No. 2 (2018)
  • Eigenvalues of elliptic operators with density
    • Authors: Bruno Colbois; Luigi Provenzano
      Abstract: We consider eigenvalue problems for elliptic operators of arbitrary order 2m subject to Neumann boundary conditions on bounded domains of the Euclidean N-dimensional space. We study the dependence of the eigenvalues upon variations of mass density. In particular we discuss the existence and characterization of upper and lower bounds under both the condition that the total mass is fixed and the condition that the \(L^{\frac{N}{2m}}\) -norm of the density is fixed. We highlight that the interplay between the order of the operator and the space dimension plays a crucial role in the existence of eigenvalue bounds.
      PubDate: 2018-02-13
      DOI: 10.1007/s00526-018-1307-0
      Issue No: Vol. 57, No. 2 (2018)
  • Nodal solutions for a supercritical semilinear problem with variable
    • Authors: Daomin Cao; Shuanglong Li; Zhongyuan Liu
      Abstract: In this paper, we are concerned with the following nonlinear supercritical elliptic problem with variable exponent, $$\begin{aligned} {\left\{ \begin{array}{ll} -\,\Delta u= u ^{2^*+ x ^\alpha -2}u,~&{}\text {in}~ B_1(0),\\ u=0,\quad &{}\text {on} ~\partial B_1(0), \end{array}\right. } \end{aligned}$$ where \(2^*=\frac{2N}{N-2}\) , \(0<\alpha <\min \{\frac{N}{2},N-2\}\) , and \(B_1(0)\) is the unit ball in \(\mathbb {R}^N\) , \(N\ge 3\) . For any \(k\in \mathbb {N}\) , we find, by variational methods, a pair of nodal solutions for this problem, which has exactly k nodal points.
      PubDate: 2018-02-13
      DOI: 10.1007/s00526-018-1305-2
      Issue No: Vol. 57, No. 2 (2018)
  • On a non-smooth potential analysis for Hörmander-type operators
    • Authors: Giulio Tralli; Francesco Uguzzoni
      Abstract: We develop a potential theory approach for some degenerate parabolic operators in non-divergence form and with non-smooth coefficients, which are modeled on smooth Hörmander vector fields. We prove necessary and sufficient Wiener-type tests for the regularity of boundary points. As a consequence we obtain, in particular, a cone-type criterion. We also investigate the related boundary value problem and the Hölder regularity at the boundary.
      PubDate: 2018-02-13
      DOI: 10.1007/s00526-018-1301-6
      Issue No: Vol. 57, No. 2 (2018)
  • Continuity of nonlinear eigenvalues in $${{\mathrm{CD}}}(K,\infty )$$ CD (
           K , ∞ ) spaces with respect to measured Gromov–Hausdorff convergence
    • Authors: Luigi Ambrosio; Shouhei Honda; Jacobus W. Portegies
      Abstract: In this note we prove in the nonlinear setting of \({{\mathrm{CD}}}(K,\infty )\) spaces the stability of the Krasnoselskii spectrum of the Laplace operator \(-\,\Delta \) under measured Gromov–Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of \({{\mathrm{CD}}}^*(K,N)\) metric measure spaces with uniformly bounded diameter. Additionally, we show that every element \(\lambda \) in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial u satisfying the eigenvalue equation \(-\, \Delta u = \lambda u\) .
      PubDate: 2018-02-12
      DOI: 10.1007/s00526-018-1315-0
      Issue No: Vol. 57, No. 2 (2018)
  • Complete $$\lambda $$ λ -hypersurfaces of weighted volume-preserving mean
           curvature flow
    • Authors: Qing-Ming Cheng; Guoxin Wei
      Abstract: In this paper, we introduce a special class of hypersurfaces which are called \(\lambda \) -hypersurfaces related to a weighted volume preserving mean curvature flow in the Euclidean space. We prove that \(\lambda \) -hypersurfaces are critical points of the weighted area functional for the weighted volume-preserving variations. Furthermore, we classify complete \(\lambda \) -hypersurfaces with polynomial area growth and \(H-\lambda \ge 0\) . The classification result generalizes the results of Huisken (J Differ Geom 31:285–299, 1990) and Colding and Minicozzi (Ann Math 175:755–833, 2012).
      PubDate: 2018-02-12
      DOI: 10.1007/s00526-018-1303-4
      Issue No: Vol. 57, No. 2 (2018)
  • The $$C^{2,\alpha }$$ C 2 , α -estimate for conical Kähler–Ricci flow
    • Authors: Liangming Shen
      Abstract: In this note, we establish a parabolic version of Tian’s \(C^{2,\alpha }\) -estimate for conical complex Monge–Ampere equations (Tian in Chin Ann Math Ser B 38(2):687–694, 2017), which includes conical Kähler–Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical Kähler–Ricci flow in Shen (J Reine Angew Math, [28]).
      PubDate: 2018-02-12
      DOI: 10.1007/s00526-018-1308-z
      Issue No: Vol. 57, No. 2 (2018)
  • Law of large numbers in CAT(1)-spaces of small radii
    • Authors: Takumi Yokota
      Abstract: We prove the law of large numbers formulated with barycenter of probability measures for random variables with values in small balls in CAT(1)-spaces. This extends the previous results in CAT(0)-spaces and CAT(1)-spaces of small diameters by Sturm and Ohta–Pálfia.
      PubDate: 2018-02-12
      DOI: 10.1007/s00526-018-1310-5
      Issue No: Vol. 57, No. 2 (2018)
  • Sharp conditions for the existence of boundary blow-up solutions to the
           Monge–Ampère equation
    • Authors: Xuemei Zhang; Yihong Du
      Abstract: In this paper we give sharp conditions on K(x) and f(u) for the existence of strictly convex solutions to the boundary blow-up Monge–Ampère problem $$\begin{aligned} M[u](x)=K(x)f(u) \quad \hbox {for } x \in \Omega ,\; u(x)\rightarrow +\,\infty \quad \hbox {as } \mathrm{dist}(x,\partial \Omega )\rightarrow 0. \end{aligned}$$ Here \(M[u]=\det \, (u_{x_{i}x_{j}})\) is the Monge–Ampère operator, and \(\Omega \) is a smooth, bounded, strictly convex domain in \( \mathbb {R}^N \, (N\ge 2)\) . Further results are obtained for the special case that \(\Omega \) is a ball. Our approach is largely based on the construction of suitable sub- and super-solutions.
      PubDate: 2018-02-10
      DOI: 10.1007/s00526-018-1312-3
      Issue No: Vol. 57, No. 2 (2018)
  • Generalized Matsushima’s theorem and Kähler–Einstein cone
    • Authors: Long Li; Kai Zheng
      Abstract: In this paper, we first prove a generalized Matsushima’s theorem, i.e. the automorphism group is reductive on a Fano manifold admitting Kähler–Einstein metrics with cone singularities along a smooth divisor. Note that the divisor in our paper is not necessarily proportional to the anti-canonical class. We then give an alternative proof of uniqueness of Kähler–Einstein cone metrics by combining the reductivity of the automorphism group with the continuity method, the approximation trick and the bifurcation technique. Moreover, our method provides an existence theorem of Kähler–Einstein cone metrics with respect to conic Ding functional.
      PubDate: 2018-02-10
      DOI: 10.1007/s00526-018-1313-2
      Issue No: Vol. 57, No. 2 (2018)
  • A curvature flow in the plane with a nonlocal term
    • Authors: Luis A. Caffarelli; Hui Yu
      Abstract: We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time asymptotics of this flow.
      PubDate: 2018-02-09
      DOI: 10.1007/s00526-018-1311-4
      Issue No: Vol. 57, No. 2 (2018)
  • 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.
      PubDate: 2018-01-10
      DOI: 10.1007/s00526-017-1298-2
      Issue No: Vol. 57, No. 1 (2018)
School of Mathematical and Computer Sciences
Heriot-Watt University
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