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MATHEMATICS (711 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: 4)
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: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
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: 19)
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: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
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: 6)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
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)
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: 5)
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: 4)
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   (Followers: 1)
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: 2)
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: 7)
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: 2)
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
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: 19)
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  
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: 13)
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: 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: 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 Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)

        1 2 3 4 | Last

Journal Cover
Calculus of Variations and Partial Differential Equations
Journal Prestige (SJR): 3.352
Citation Impact (citeScore): 2
Number of Followers: 0  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0835 - ISSN (Online) 0944-2669
Published by Springer-Verlag Homepage  [2350 journals]
  • On small traveling waves to the mass critical fractional NLS
    • Authors: Ivan Naumkin; Pierre Raphaël
      Abstract: We consider the mass critical fractional (NLS) $$\begin{aligned} i\partial _{t}u-\left D\right ^{s}u+u\left u\right ^{2s}=0,\text { }x\in \mathbb {R},\text { }1<s<2. \end{aligned}$$ We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associated profiles in the small mass limit. We therefore recover a situation similar to the one discovered in Gérard et al (A two soliton with transient turbulent regime for the one dimensional cubic half wave, 2018) for the critical case \(s=1\) , but with a completely different asymptotic profile when the mass vanishes.
      PubDate: 2018-05-16
      DOI: 10.1007/s00526-018-1355-5
      Issue No: Vol. 57, No. 3 (2018)
  • Quantitative uniqueness of solutions to second order elliptic equations
           with singular potentials in two dimensions
    • Authors: Blair Davey; Jiuyi Zhu
      Abstract: In this article, we study the vanishing order of solutions to second order elliptic equations with singular lower order terms in the plane. In particular, we derive lower bounds for solutions on arbitrarily small balls in terms of the Lebesgue norms of the lower order terms for all admissible exponents. Then we show that a scaling argument allows us to pass from these vanishing order estimates to estimates for the rate of decay of solutions at infinity. Our proofs rely on a new \(L^p - L^q\) Carleman estimate for the Laplacian in \(\mathbb {R}^2\) .
      PubDate: 2018-05-11
      DOI: 10.1007/s00526-018-1345-7
      Issue No: Vol. 57, No. 3 (2018)
  • Existence of solutions to a general geometric elliptic variational problem
    • Authors: Yangqin Fang; Sławomir Kolasiński
      Abstract: We consider the problem of minimising an inhomogeneous anisotropic elliptic functional in a class of closed m dimensional subsets of  \({\mathbf {R}}^n\) which is stable under taking smooth deformations homotopic to the identity and under local Hausdorff limits. We prove that the minimiser exists inside the class and is an \(({\mathscr {H}}^m,m)\)  rectifiable set in the sense of Federer. The class of competitors encodes a notion of spanning a boundary. We admit unrectifiable and non-compact competitors and boundaries, and we make no restrictions on the dimension m and the co-dimension \(n-m\) other than \(1 \le m < n\) . An important tool for the proof is a novel smooth deformation theorem. The skeleton of the proof and the main ideas follow Almgren’s (Ann Math (2) 87:321–391, 1968) paper. In the end we show that classes of sets spanning some closed set B in homological and cohomological sense satisfy our axioms.
      PubDate: 2018-05-11
      DOI: 10.1007/s00526-018-1348-4
      Issue No: Vol. 57, No. 3 (2018)
  • An extension of Jörgens–Calabi–Pogorelov theorem to parabolic
           Monge–Ampère equation
    • Authors: Wei Zhang; Jiguang Bao; Bo Wang
      Abstract: We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension \(n\ge 3\) , the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations.
      PubDate: 2018-05-09
      DOI: 10.1007/s00526-018-1363-5
      Issue No: Vol. 57, No. 3 (2018)
  • Existence and multiplicity for elliptic p-Laplacian problems with critical
           growth in the gradient
    • Authors: Colette De Coster; Antonio J. Fernández
      Abstract: We consider the boundary value problem where \(\Omega \subset \mathbb {R}^{N}\) , \(N \ge 2\) , is a bounded domain with smooth boundary. We assume \(c,\, h \in L^q(\Omega )\) for some \(q > \max \{N/p,1\}\) with \(c \gneqq 0\) and \(\mu \in L^{\infty }(\Omega )\) . We prove existence and uniqueness results in the coercive case \( \lambda \le 0\) and existence and multiplicity results in the non-coercive case \( \lambda >0\) . Also, considering stronger assumptions on the coefficients, we clarify the structure of the set of solutions in the non-coercive case.
      PubDate: 2018-05-05
      DOI: 10.1007/s00526-018-1346-6
      Issue No: Vol. 57, No. 3 (2018)
  • On the Lipschitz character of orthotropic p -harmonic functions
    • Authors: P. Bousquet; L. Brasco; C. Leone; A. Verde
      Abstract: We prove that local weak solutions of the orthotropic p-harmonic equation are locally Lipschitz, for every \(p\ge 2\) and in every dimension. More generally, the result holds true for more degenerate equations with orthotropic structure, with right-hand sides in suitable Sobolev spaces.
      PubDate: 2018-05-05
      DOI: 10.1007/s00526-018-1349-3
      Issue No: Vol. 57, No. 3 (2018)
  • On Ambrosetti–Malchiodi–Ni conjecture on two-dimensional
           smooth bounded domains
    • Authors: Suting Wei; Bin Xu; Jun Yang
      Abstract: We consider the problem $$\begin{aligned} \epsilon ^2 \Delta u-V(y)u+u^p\,=\,0,\quad u>0\quad \text{ in }\quad \Omega , \quad \frac{\partial u}{\partial \nu }\,=\,0\quad \text{ on }\quad \partial \Omega , \end{aligned}$$ where \(\Omega \) is a bounded domain in \({\mathbb {R}}^2\) with smooth boundary, the exponent p is greater than 1, \(\epsilon >0\) is a small parameter, V is a uniformly positive, smooth potential on \(\bar{\Omega }\) , and \(\nu \) denotes the outward unit normal of \(\partial \Omega \) . Let \(\Gamma \) be a curve intersecting orthogonally \(\partial \Omega \) at exactly two points and dividing \(\Omega \) into two parts. Moreover, \(\Gamma \) satisfies stationary and non-degeneracy conditions with respect to the functional \(\int _{\Gamma }V^{\sigma }\) , where \(\sigma =\frac{p+1}{p-1}-\frac{1}{2}\) . We prove the existence of a solution \(u_\epsilon \) concentrating along the whole of \(\Gamma \) , exponentially small in \(\epsilon \) at any fixed distance from it, provided that \(\epsilon \) is small and away from certain critical numbers. In particular, this establishes the validity of the two dimensional case of a conjecture by Ambrosetti et al. (Indiana Univ Math J 53(2), 297–329, 2004).
      PubDate: 2018-05-04
      DOI: 10.1007/s00526-018-1347-5
      Issue No: Vol. 57, No. 3 (2018)
  • Generalization of unfolding operator for highly oscillating smooth
           boundary domains and homogenization
    • Authors: S. Aiyappan; A. K. Nandakumaran; Ravi Prakash
      Abstract: Unfolding operators have been introduced and used to study homogenization problems. Initially, they were introduced for problems with rapidly oscillating coefficients and porous domains. Later, this has been developed for domains with oscillating boundaries, typically with rectangular or pillar type boundaries which are classified as non-smooth. In this article, we develop new unfolding operators, where the oscillations can be smooth and hence they have wider applications. We have demonstrated by developing unfolding operators for circular domains with rapid oscillations with high amplitude of O(1) to study the homogenization of an elliptic problem.
      PubDate: 2018-05-04
      DOI: 10.1007/s00526-018-1354-6
      Issue No: Vol. 57, No. 3 (2018)
  • Partial regularity for a nonlinear sigma model with gravitino in higher
    • Authors: Jürgen Jost; Ruijun Wu; Miaomiao Zhu
      Abstract: We study the regularity problem of the nonlinear sigma model with gravitino fields in higher dimensions. After setting up the geometric model, we derive the Euler–Lagrange equations and consider the regularity of weak solutions defined in suitable Sobolev spaces. We show that any weak solution is actually smooth under some smallness assumption for certain Morrey norms. By assuming some higher integrability of the vector spinor, we can show a partial regularity result for stationary solutions, provided the gravitino is critical, which means that the corresponding supercurrent vanishes. Moreover, in dimension \(<6\) , partial regularity holds for stationary solutions with respect to general gravitino fields.
      PubDate: 2018-05-03
      DOI: 10.1007/s00526-018-1366-2
      Issue No: Vol. 57, No. 3 (2018)
  • Concentration-compactness principle for Trudinger–Moser inequalities on
           Heisenberg groups and existence of ground state solutions
    • Authors: Jungang Li; Guozhen Lu; Maochun Zhu
      Abstract: Let \(\mathbb {H}^{n}=\mathbb {C}^{n}\times \mathbb {R}\) be the n-dimensional Heisenberg group, \(Q=2n+2\) be the homogeneous dimension of \(\mathbb {H}^{n}\) . We extend the well-known concentration-compactness principle on finite domains in the Euclidean spaces of Lions (Rev Mat Iberoam 1:145–201, 1985) to the setting of the Heisenberg group \(\mathbb {H}^{n}\) . Furthermore, we also obtain the corresponding concentration-compactness principle for the Sobolev space \({ HW}^{1,Q}(\mathbb {H}^{n}) \) on the entire Heisenberg group \(\mathbb {H}^{n}\) . Our results improve the sharp Trudinger–Moser inequality on domains of finite measure in \(\mathbb {H}^{n}\) by Cohn and Lu (Indiana Univ Math J 50(4):1567–1591, 2001) and the corresponding one on the whole space \(\mathbb {H}^n\) by Lam and Lu (Adv Math 231:3259–3287, 2012). All the proofs of the concentration-compactness principles for the Trudinger–Moser inequalities in the literature even in the Euclidean spaces use the rearrangement argument and the Polyá–Szegö inequality. Due to the absence of the Polyá–Szegö inequality on the Heisenberg group, we will develop a different argument. Our approach is surprisingly simple and general and can be easily applied to other settings where symmetrization argument does not work. As an application of the concentration-compactness principle, we establish the existence of ground state solutions for a class of Q- Laplacian subelliptic equations on \(\mathbb {H}^{n}\) : $$\begin{aligned} -\mathrm {div}\left( \left \nabla _{\mathbb {H}}u\right ^{Q-2} \nabla _{\mathbb {H}}u\right) +V(\xi ) \left u\right ^{Q-2}u=\frac{f(u) }{\rho (\xi )^{\beta }} \end{aligned}$$ with nonlinear terms f of maximal exponential growth \(\exp (\alpha t^{\frac{Q}{Q-1}})\) as \(t\rightarrow +\infty \) . All the results proved in this paper hold on stratified groups with the same proofs. Our method in this paper also provide a new proof of the classical concentration-compactness principle for Trudinger-Moser inequalities in the Euclidean spaces without using the symmetrization argument.
      PubDate: 2018-05-02
      DOI: 10.1007/s00526-018-1352-8
      Issue No: Vol. 57, No. 3 (2018)
  • Sharp regularity estimates for quasi-linear elliptic dead core problems
           and applications
    • Authors: João Vítor da Silva; Ariel M. Salort
      Abstract: In this manuscript we study geometric regularity estimates for quasi-linear elliptic equations of p-Laplace type ( \(1< p< \infty \) ) with strong absorption condition: $$\begin{aligned} -\mathrm {div}(\Phi (x, u, \nabla u)) + \lambda _0(x) u_{+}^q(x) = 0 \quad \hbox {in} \quad \Omega \subset \mathbb {R}^N, \end{aligned}$$ where \(\Phi : \Omega \times \mathbb {R}_{+} \times \mathbb {R}^N \rightarrow \mathbb {R}^N\) is a vector field with an appropriate p-structure, \(\lambda _0\) is a non-negative and bounded function and \(0\le q<p-1\) . Such a model permits existence of solutions with dead core zones, i.e, a priori unknown regions where non-negative solutions vanish identically. We establish sharp and improved \(C^{\gamma }\) regularity estimates along free boundary points, namely \(\mathfrak {F}_0(u, \Omega ) = \partial \{u>0\} \cap \Omega \) , where the regularity exponent is given explicitly by \(\gamma = \frac{p}{p-1-q} \gg 1\) . Some weak geometric and measure theoretical properties as non-degeneracy, uniform positive density and porosity of free boundary are proved. As an application, a Liouville-type result for entire solutions is established provided that their growth at infinity can be controlled in an appropriate manner. Finally, we obtain finiteness of \((N-1)\) -Hausdorff measure of free boundary for a particular class of dead core problems. The approach employed in this article is novel even to dead core problems governed by the p-Laplace operator \(-\Delta _p u + \lambda _0 u^q\chi _{\{u>0\}} = 0\) for any \(\lambda _0>0\) .
      PubDate: 2018-04-30
      DOI: 10.1007/s00526-018-1344-8
      Issue No: Vol. 57, No. 3 (2018)
  • General transport problems with branched minimizers as functionals of
           1-currents with prescribed boundary
    • Authors: Alessio Brancolini; Benedikt Wirth
      Abstract: A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a given final distribution. The cost of the scheme encodes a higher transport efficiency the more mass is moved together, which automatically leads to optimal transportation networks with a hierarchical branching structure. The two major existing model formulations use either mass fluxes (vector-valued measures, Eulerian formulation) or patterns (probabilities on the space of particle paths, Lagrangian formulation). In the branched transport problem the transportation cost is a fractional power of the transported mass. In this paper we instead analyse the much more general class of transport problems in which the transportation cost is merely a nonnegative increasing and subadditive function (in a certain sense this is the broadest possible generalization of branched transport). In particular, we address the problem of the equivalence of the above-mentioned formulations in this wider context. However, the newly-introduced class of transportation costs lacks strict concavity which complicates the analysis considerably. New ideas are required, in particular, it turns out convenient to state the problem via 1-currents. Our analysis also includes the well-posedness, some network properties, as well as a metrization and a length space property of the model cost, which were previously only known for branched transport. Some already existing arguments in that field are given a more concise and simpler form.
      PubDate: 2018-04-30
      DOI: 10.1007/s00526-018-1364-4
      Issue No: Vol. 57, No. 3 (2018)
  • Maximization of the total population in a reaction–diffusion model
           with logistic growth
    • Authors: Kentaro Nagahara; Eiji Yanagida
      Abstract: This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the effect of spatial heterogeneity on the total population of a biological species at a steady state, using a reaction–diffusion logistic model. Our objective is to maximize the total population when resources are distributed in the habitat to control the intrinsic growth rate, but the total amount of resources is limited. It is shown that under some conditions, any local maximizer must be of “bang–bang” type, which gives a partial answer to the conjecture addressed by Ding et al. (Nonlinear Anal Real World Appl 11(2):688–704, 2010). To this purpose, we compute the first and second variations of the total population. When the growth rate is not of bang–bang type, it is shown in some cases that the first variation becomes nonzero and hence the resource distribution is not a local maximizer. When the first variation becomes zero, we prove that the second variation is positive. These results implies that the bang–bang property is essential for the maximization of total population.
      PubDate: 2018-04-28
      DOI: 10.1007/s00526-018-1353-7
      Issue No: Vol. 57, No. 3 (2018)
  • Uniqueness of self-shrinkers to the degree-one curvature flow with a
           tangent cone at infinity
    • Authors: Siao-Hao Guo
      Abstract: Given a smooth, symmetric and homogeneous of degree one function \(f\left( \lambda _{1},\ldots ,\lambda _{n}\right) \) satisfying \(\partial _{i}f>0\quad \forall \,i=1,\ldots , n\) , and a properly embedded smooth cone \({\mathcal {C}}\) in \({\mathbb {R}}^{n+1}\) , we show that under suitable conditions on f, there is at most one f self-shrinker (i.e. a hypersurface \(\Sigma \) in \({\mathbb {R}}^{n+1}\) satisfying \(f\left( \kappa _{1},\ldots ,\kappa _{n}\right) +\frac{1}{2}X\cdot N=0\) , where \(\kappa _{1},\ldots ,\kappa _{n}\) are principal curvatures of \(\Sigma \) ) that is asymptotic to the given cone \({\mathcal {C}}\) at infinity.
      PubDate: 2018-04-28
      DOI: 10.1007/s00526-018-1356-4
      Issue No: Vol. 57, No. 3 (2018)
  • On nonlinear cross-diffusion systems: an optimal transport approach
    • Authors: Inwon Kim; Alpár Richárd Mészáros
      Abstract: We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of discrete-time solutions. Its continuum limit, due to the possible mixing of the densities, only solves a weaker version of the original system. In one space dimension, we find a stable initial configuration which allows the densities to be segregated. This leads to the evolution of a stable interface between the two densities, and to a stronger convergence result to the continuum limit. In particular derivation of a standard weak solution to the system is available. We also study the incompressible limit of the system, which addresses transport under a height constraint on the total density. In one space dimension we show that the problem leads to a two-phase Hele-Shaw type flow.
      PubDate: 2018-04-28
      DOI: 10.1007/s00526-018-1351-9
      Issue No: Vol. 57, No. 3 (2018)
  • Uniqueness and symmetry of ground states for higher-order equations
    • Authors: Woocheol Choi; Younghun Hong; Jinmyoung Seok
      Abstract: We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schrödinger and Hartree equations whose higher-order differentials have small coefficients. As an application, we obtain error estimates for higher-order approximations to the pseudo-relativistic ground state. Our proof adapts the strategy of Lenzmann (Anal PDE 2:1–27, 2009) using local uniqueness near the limit of ground states in a variational problem. However, in order to bypass difficulties from lack of symmetrization tools for higher-order differential operators, we employ the contraction mapping argument in our earlier work (Choi et al. 2017. arXiv:1705.09068) to construct radially symmetric real-valued solutions, as well as improving local uniqueness near the limit.
      PubDate: 2018-04-27
      DOI: 10.1007/s00526-018-1362-6
      Issue No: Vol. 57, No. 3 (2018)
  • Quasi-periodic two-scale homogenisation and effective spatial dispersion
           in high-contrast media
    • Authors: Shane Cooper
      Abstract: The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this assumption the (periodic) two-scale limit of the operator is insufficient to capture the full asymptotic spectral properties of high-contrast periodic media. Asymptotically, waves of all periods (or quasi-momenta) are shown to persist and an appropriate extension of the notion of two-scale convergence is introduced. As a result, homogenised limit equations with none trivial quasi-momentum dependence are found as resolvent limits of the original operator family. This results in asymptotic spectral behaviour with a rich dependence on quasimomenta.
      PubDate: 2018-04-27
      DOI: 10.1007/s00526-018-1365-3
      Issue No: Vol. 57, No. 3 (2018)
  • Weak KAM theory for discounted Hamilton–Jacobi equations and its
    • Authors: Hiroyoshi Mitake; Kohei Soga
      Abstract: Weak KAM theory for discounted Hamilton–Jacobi equations and corresponding discounted Lagrangian/Hamiltonian dynamics is developed. Then it is applied to error estimates for viscosity solutions in the vanishing discount process. The main feature is to introduce and investigate the family of \(\alpha \) -limit points of minimizing curves, with some details in terms of minimizing measures. In error estimates, the family of \(\alpha \) -limit points is effectively exploited with properties of the corresponding dynamical systems.
      PubDate: 2018-04-27
      DOI: 10.1007/s00526-018-1359-1
      Issue No: Vol. 57, No. 3 (2018)
  • Existence of tangent lines to Carnot–Carathéodory geodesics
    • Authors: Roberto Monti; Alessandro Pigati; Davide Vittone
      Abstract: We show that length minimizing curves in Carnot–Carathéodory spaces possess at any point at least one tangent curve (i.e., a blow-up in the nilpotent approximation) equal to a straight horizontal line.
      PubDate: 2018-04-27
      DOI: 10.1007/s00526-018-1361-7
      Issue No: Vol. 57, No. 3 (2018)
  • Quasilinear equations with natural growth in the gradients in spaces of
           Sobolev multipliers
    • Authors: Karthik Adimurthi; Cong Phuc Nguyen
      Abstract: We study the existence problem for a class of nonlinear elliptic equations whose prototype is of the form \(-\Delta _p u = \nabla u ^p + \sigma \) in a bounded domain \(\Omega \subset \mathbb {R}^n\) . Here \(\Delta _p\) , \(p>1\) , is the standard p-Laplacian operator defined by \(\Delta _p u=\mathrm{div}\, ( \nabla u ^{p-2}\nabla u)\) , and the datum \(\sigma \) is a signed distribution in \(\Omega \) . The class of solutions that we are interested in consists of functions \(u\in W^{1,p}_0(\Omega )\) such that \( \nabla u \in M(W^{1,p}(\Omega )\rightarrow L^p(\Omega ))\) , a space pointwise Sobolev multipliers consisting of functions \(f\in L^{p}(\Omega )\) such that $$\begin{aligned} \int _{\Omega } f ^{p} \varphi ^p dx \le C \int _{\Omega } ( \nabla \varphi ^p + \varphi ^p) dx \quad \forall \varphi \in C^\infty (\Omega ), \end{aligned}$$ for some \(C>0\) . This is a natural class of solutions at least when the distribution \(\sigma \) is nonnegative and compactly supported in \(\Omega \) . We show essentially that, with only a gap in the smallness constants, the above equation has a solution in this class if and only if one can write \(\sigma =\mathrm{div}\, F\) for a vector field F such that \( F ^{\frac{1}{p-1}}\in M(W^{1,p}(\Omega )\rightarrow L^p(\Omega ))\) . As an important application, via the exponential transformation \(u\mapsto v=e^{\frac{u}{p-1}}\) , we obtain an existence result for the quasilinear equation of Schrödinger type \(-\Delta _p v = \sigma \, v^{p-1}\) , \(v\ge 0\) in \(\Omega \) , and \(v=1\) on \(\partial \Omega \) , which is interesting in its own right.
      PubDate: 2018-04-27
      DOI: 10.1007/s00526-018-1357-3
      Issue No: Vol. 57, No. 3 (2018)
School of Mathematical and Computer Sciences
Heriot-Watt University
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