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  Subjects -> MATHEMATICS (Total: 1040 journals)
    - APPLIED MATHEMATICS (83 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (770 journals)
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    - PROBABILITIES AND MATH STATISTICS (98 journals)

MATHEMATICS (770 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     Hybrid Journal   (Followers: 38)
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: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 21)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 17)
Advances in Mathematical Physics     Open Access   (Followers: 7)
Advances in Mathematics     Full-text available via subscription   (Followers: 15)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
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: 8)
Advances in Pure Mathematics     Open Access   (Followers: 9)
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: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 2)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
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: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 3)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 7)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
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: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
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)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
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: 2)
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: 13)
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: 3)
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: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     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 Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
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)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
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: 3)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
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: 10)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
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: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
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: 4)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal  
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: 2)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  

        1 2 3 4 | Last

Similar Journals
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  [2562 journals]
  • Uniqueness of least energy solutions for Monge–Ampère
           functional
    • Abstract: Let \(\Omega \) be a bounded, smooth, uniformly convex domain in \(\mathbb {R}^n\) . We consider the following functional $$\begin{aligned} \mathcal {E}[u]=\int _{\Omega }(-u)\det D^2 u dx,\quad \Vert u\Vert _{L^{q+1}(\Omega )}=1 \qquad \qquad (0.1) \end{aligned}$$ where \(u\in C^2(\bar{\Omega })\) is convex and \(u=0\) on \(\partial \Omega \) . In this paper, the uniqueness of least energy solution of (0.1) is investigated. For \(n=2\) , we prove the least energy solution of (0.1) is unique for \(2<q<\infty \) provided it is locally uniformly convex. In particular, for \(q=+\infty \) , we show the uniqueness of the least energy solution of (0.1) and find its relation to Santalò point.
      PubDate: 2019-03-22
       
  • Stability of Ricci de Turck flow on singular spaces
    • Abstract: In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under an assumption of integrability, linear and tangential stability. We provide a characterization of conical singularities satisfying tangential stability and discuss examples where the integrability condition is satisfied.
      PubDate: 2019-03-22
       
  • Topological singular set of vector-valued maps, I: applications to
           manifold-constrained Sobolev and BV spaces
    • Abstract: We introduce an operator  \(\mathbf {S}\) on vector-valued maps u which has the ability to capture the relevant topological information carried by u. In particular, this operator is defined on maps that take values in a closed submanifold  \(\mathscr {N}\) of the Euclidean space  \(\mathbb {R}^m\) , and coincides with the distributional Jacobian in case  \(\mathscr {N}\) is a sphere. More precisely, the range of  \(\mathbf {S}\) is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. In this paper, we use  \(\mathbf {S}\) to characterise strong limits of smooth, \(\mathscr {N}\) -valued maps with respect to Sobolev norms, extending a result by Pakzad and Rivière. We also discuss applications to the study of manifold-valued maps of bounded variation. In a companion paper, we will consider applications to the asymptotic behaviour of minimisers of Ginzburg–Landau type functionals, with \(\mathscr {N}\) -well potentials.
      PubDate: 2019-03-21
       
  • Solution of the tangential Kohn Laplacian on a class of non-compact CR
           manifolds
    • Abstract: We solve \(\square _b\) on a class of non-compact 3-dimensional strongly pseudoconvex CR manifolds via a certain conformal equivalence. The idea is to make use of a related \(\square _b\) operator on a compact 3-dimensional strongly pseudoconvex CR manifold, which we solve using a pseudodifferential calculus. The way we solve \(\square _b\) works whenever \({\overline{\partial }}_b\) on the compact CR manifold has closed range in \(L^2\) ; in particular, as in Beals and Greiner (Calculus on Heisenberg manifolds. Annals of mathematics studies, vol 119. Princeton University Press, Princeton, 1988), it does not require the CR manifold to be the boundary of a strongly pseudoconvex domain in \({\mathbb {C}}^2\) . Our result provides in turn a key step in the proof of a positive mass theorem in 3-dimensional CR geometry, by Cheng et al. (Adv Math 308:276–347, 2017), which they then applied to study the CR Yamabe problem in 3 dimensions.
      PubDate: 2019-03-21
       
  • Extremals of Log Sobolev inequality on non-compact manifolds and Ricci
           soliton structures
    • Abstract: In this paper we establish the existence of extremals for the Log Sobolev functional on complete non-compact manifolds with Ricci curvature bounded from below and strictly positive injectivity radius, under a condition near infinity. This extends a previous result by Q. Zhang where a \(C^1\) bound on the whole Riemann tensor was assumed. When Ricci curvature is also bounded from above we get exponential decay at infinity of the extremals. As a consequence of these analytical results we establish, under the same assumptions, that non-trivial shrinking Ricci solitons support a gradient Ricci soliton structure. On the way, we prove two results of independent interest: the existence of a distance-like function with uniformly controlled gradient and Hessian on complete non-compact manifolds with bounded Ricci curvature and strictly positive injectivity radius and a general growth estimate for the norm of the soliton vector field. This latter is based on a new Toponogov type lemma for manifolds with bounded Ricci curvature, and represents the first known growth estimate for the whole norm of the soliton field in the non-gradient case.
      PubDate: 2019-03-20
       
  • Lower bounds for the first eigenvalue of the Steklov problem on graphs
    • Abstract: We give lower bounds for the first non-zero Steklov eigenvalue on connected graphs. These bounds depend on the extrinsic diameter of the boundary and not on the diameter of the graph. We obtain a lower bound which is sharp when the cardinal of the boundary is 2, and asymptotically sharp as the diameter of the boundary tends to infinity in the other cases. We also investigate the case of weighted graphs and compare our result to the Cheeger inequality.
      PubDate: 2019-03-20
       
  • Lifting of $${\mathbb {RP}^{d-1}}$$ RP d - 1 -valued maps in BV and
           applications to uniaxial Q -tensors. With an appendix on an intrinsic BV
           -energy for manifold-valued maps
    • Abstract: We prove that a BV map with values into the projective space \({\mathbb {RP}^{d-1}}\) has a BV lifting with values into the unit sphere \({{\mathbb {S}}^{d-1}}\) that satisfies an optimal BV-estimate. As an application to liquid crystals, this result is also stated for BV maps with values into the set of uniaxial Q-tensors. In order to quantify BV liftings, we prove an explicit formula for an intrinsic BV-energy of maps with values into any compact smooth manifold.
      PubDate: 2019-03-20
       
  • Metric currents and the Poincaré inequality
    • Abstract: We show that a complete doubling metric space \((X,d,\mu )\) supports a weak 1-Poincaré inequality if and only if it admits a pencil of curves (PC) joining any pair of points \(s,t \in X\) . This notion was introduced by S. Semmes in the 90’s, and has been previously known to be a sufficient condition for the weak 1-Poincaré inequality. Our argument passes through the intermediate notion of a generalised pencil of curves (GPC). A GPC joining s and t is a normal 1-current T, in the sense of Ambrosio and Kirchheim, with boundary \(\partial T = \delta _{t} - \delta _{s}\) , support contained in a ball of radius \(\sim d(s,t)\) around \(\{s,t\}\) , and satisfying \(\Vert T\Vert \ll \mu \) , with $$\begin{aligned} \frac{d\Vert T\Vert }{d\mu }(y) \lesssim \frac{d(s,y)}{\mu (B(s,d(s,y)))} + \frac{d(t,y)}{\mu (B(t,d(t,y)))}. \end{aligned}$$ We show that the 1-Poincaré inequality implies the existence of GPCs joining any pair of points in X. Then, we deduce the existence of PCs from a recent decomposition result for normal 1-currents due to Paolini and Stepanov.
      PubDate: 2019-03-20
       
  • Invariance of critical points under Kelvin transform and multiple
           solutions in exterior domains of $$\mathbb {R}^2$$ R 2
    • Abstract: Let \(\Omega ={\mathbb {R}}^2{\setminus }\overline{B(0,1)}\) be the exterior of the closed unit ball. We prove the existence of extremal constant-sign solutions as well as sign-changing solutions of the following boundary value problem $$\begin{aligned} -\Delta u=a(x) f(u)\ \text{ in } \Omega ,\quad u=0\ \text{ on } \partial \Omega =\partial B(0,1), \end{aligned}$$ where the nonnegative coefficient a satisfies a certain integrability condition. We are looking for solutions in the space \(D^{1,2}_0(\Omega )\) which is the completion of \(C^\infty _c(\Omega )\) with respect to the \(\Vert \nabla \cdot \Vert _{2,\Omega }\) -norm. Unlike in the situation of \({\mathbb {R}}^N\) with \(N\ge 3\) , the behavior of solutions in the borderline case \(N=2\) considered here is qualitatively significantly different, such as for example, constant-sign solutions in the borderline case are not decaying to zero at infinity, and instead are bounded away from zero. Our main tool in studying the above problem will be the Kelvin transform. We will first show that the Kelvin transform provides an isometric isomorphism between \(D^{1,2}_0(\Omega )\) and the Sobolev space \(H^1_0(B(0,1))\) , which is order-preserving. This allows us to establish a one-to-one mapping between solutions of the problem above and solutions of an associated problem in the bounded domain B(0, 1) of the form: $$\begin{aligned} -\Delta u=b(x) f(u)\ \text{ in } B(0,1),\quad u=0\ \text{ on } \partial B(0,1), \end{aligned}$$ where b satisfies an integrability condition in terms of the coefficient a. This duality approach given via the Kelvin transform allows us to handle nonlinearities under sub, super or asymptotically linear hypotheses.
      PubDate: 2019-03-20
       
  • Existence of positive solution of the equation $$(-\Delta )^{s}u+a(x)u= u
           ^{2^{*}_{s}-2}u$$ ( - Δ ) s u + a ( x ) u = u 2 s ∗ - 2 u
    • Abstract: In this paper we show existence of positive solution to the problem In order to prove the main result, we study a limit problem of (P). More precisely, we study the case when \(a=0\) . Moreover, we prove the version to \({\mathbb {R}}^{N}\) of Struwe’s Global compactness result [14] for fractional Laplace operator.
      PubDate: 2019-03-20
       
  • The anisotropic polyharmonic curve flow for closed plane curves
    • Abstract: We study the curve diffusion flow for closed curves immersed in the Minkowski plane \({\mathcal {M}}\) , which is equivalent to the Euclidean plane endowed with a closed, symmetric, convex curve called an indicatrix that scales the length of a vector in \({\mathcal {M}}\) depending on its length. The indiactrix \(\partial {\mathcal {U}}\) (where \({\mathcal {U}}\subset {\mathbb {R}}^{2}\) is a convex, centrally symmetric domain) induces a second convex body, the isoperimetrix \(\tilde{{\mathcal {I}}}\) . This set is the unique convex set that miniminises the isoperimetric ratio (modulo homothetic rescaling) in the Minkowski plane. We prove that under the flow, closed curves that are initially close to a homothetic rescaling of the isoperimetrix in an averaged \(L^{2}\) sense exists for all time and converge exponentially fast to a homothetic rescaling of the isoperimetrix that has enclosed area equal to the enclosed area of the initial immersion.
      PubDate: 2019-03-20
       
  • Spectral shape optimization for the Neumann traces of the
           Dirichlet-Laplacian eigenfunctions
    • Abstract: We consider a spectral optimal design problem involving the Neumann traces of the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset \(\Omega \) of . The cost functional measures the amount of energy that Dirichlet eigenfunctions concentrate on the boundary and that can be recovered with a bounded density function. We first prove that, assuming a \(L^1\) constraint on densities, the so-called Rellich functions maximize this functional. Motivated by several issues in shape optimization or observation theory where it is relevant to deal with bounded densities, and noticing that the \(L^\infty \) -norm of Rellich functions may be large, depending on the shape of \(\Omega \) , we analyze the effect of adding pointwise constraints when maximizing the same functional. We investigate the optimality of bang–bang functions and Rellich densities for this problem. We also deal with similar issues for a close problem, where the cost functional is replaced by a spectral approximation. Finally, this study is completed by the investigation of particular geometries and is illustrated by several numerical simulations.
      PubDate: 2019-03-20
       
  • The convergence of the mean field type flow at a critical case
    • Abstract: Let (M, g) be a closed Riemann surface. Castéras (Pac J Math 276:321–345, 2015) introduced a mean field type flow and obtained its global existence. For \(\rho \ne 8N\pi \) , assuming in addition that \(J_\rho (v(t))\ge -C\) for \(\rho >8\pi \) , they showed the convergence of the flow. In this paper, we will prove the convergence of the flow for the critical case \(\rho =8\pi \) with some appropriate initial data \(v_0\) and some geometric hypothesis. In particular, this gives a new proof of Ding–Jost–Li–Wang’s result in (Asian J Math 1:230–248, 1997).
      PubDate: 2019-03-19
       
  • Symmetry and approximate symmetry of a nonlinear elliptic problem over a
           ring
    • Abstract: A singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand concerns a solution of the equation \(\Delta u = f(u)\) in a domain \(\Omega \) subject to constant boundary data, where the function f in general is not monotone. When the domain \(\Omega \) is a perfect ring, we incorporate a new idea of radial correction into the classical moving plane method to prove the radial symmetry of a solution. When the domain is slightly shifted from a ring, we establish the stability of the solution by showing the approximate radial symmetry of the free boundary and the solution. For this purpose, we complete the proof via an evolutionary point of view, as an elliptic comparison principle is false, nevertheless a parabolic one holds.
      PubDate: 2019-03-19
       
  • Critical exponent for the global existence of solutions to a semilinear
           heat equation with degenerate coefficients
    • Abstract: We investigate a non-homogeneous semilinear heat equation which involves degenerate coefficients. More precisely, in order to give a rather complete theory, we focus on two types of weights \(w(x)= x_1 ^a\) or \(w(x)= x ^b\) where \(a,b >0\) in a suitable range. We prove the existence of a Fujita exponent and describe the dichotomy existence/non-existence of global in time solutions. The coefficients under consideration admit either a singularity at the origin or a line of singularities. In this latter case, the problem is related to the fractional Laplacian, through the Caffarelli–Silvestre extension and is a first attempt to develop a parabolic theory in this setting.
      PubDate: 2019-03-19
       
  • The gradient flow of the potential energy on the space of arcs
    • Abstract: We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of generalized solutions to the corresponding nonlinear evolutionary PDE and their exponential decay to the equilibrium. We also observe that the system admits solutions backwards in time, which leads to non-uniqueness of trajectories.
      PubDate: 2019-03-18
       
  • Degraded mixing solutions for the Muskat problem
    • Abstract: We prove the existence of infinitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macroscopic behaviour inside the mixing zone. In fact, we estimate the volume proportion of each fluid in every rectangle of the mixing zone. The proof is a refined version of the convex integration scheme submitted in De Lellis and Székelyhidi Jr. (Arch Ration Mech Anal 195:225–260, 2010), Székelyhidi (Ann Sci Éc Norm Supér 45(3):491–509, 2012) applied to the subsolution in Castro et al. (Mixing solutions for the Muskat problem, arXiv:1605.04822, 2016). More generally, we obtain a quantitative h-principle for a class of evolution equations which shows that, in terms of weak*-continuous quantities, a generic solution in a suitable metric space essentially behaves like the subsolution. This applies of course to linear quantities, and in the case of IPM to the power balance \(\mathbf {P}\) (14) which is quadratic. As further applications of such quantitative h-principle we discuss the case of vortex sheet for the incompressible Euler equations.
      PubDate: 2019-03-08
       
  • Sobolev regularity for convex functionals on BD
    • Abstract: We establish the first Sobolev regularity and uniqueness results for minimisers of autonomous, convex variational integrals of linear growth which depend on the symmetric rather than the full gradient. This extends the results available in the literature for the BV-setting to the case of functionals whose full gradients are a priori not known to exist as finite matrix-valued Radon measures.
      PubDate: 2019-02-26
       
  • Fractional Kirchhoff problems with critical Trudinger–Moser
           nonlinearity
    • Abstract: This paper is concerned with the existence of solutions for a class of fractional Kirchhoff-type problems with Trudinger–Moser nonlinearity: $$\begin{aligned} {\left\{ \begin{array}{ll} M\left( \displaystyle \iint _{{\mathbb {R}}^{2N}}\frac{ u(x)-u(y) ^{N/s}}{ x-y ^{2N}}dxdy\right) (-\Delta )^{s}_{N/s}u=f(x,u)\,\, \ &{}\quad \mathrm{in}\ \Omega ,\\ u=0\ \ \ \ &{}\quad \mathrm{in}\ {\mathbb {R}}^N{\setminus } \Omega , \end{array}\right. } \end{aligned}$$ where \((-\Delta )^{s}_{N/s}\) is the fractional N / s-Laplacian operator, \(N\ge 1\) , \(s\in (0,1)\) , \(\Omega \subset {\mathbb {R}}^N\) is a bounded domain with Lipschitz boundary, \(M:{\mathbb {R}}^+_0\rightarrow {\mathbb {R}}^+_0\) is a continuous function, and \(f:\Omega \times {\mathbb {R}}\rightarrow {\mathbb {R}} \) is a continuous function behaving like \(\exp (\alpha t^{2})\) as \(t\rightarrow \infty \) for some \(\alpha >0\) . We first obtain the existence of a ground state solution with positive energy by using minimax techniques combined with the fractional Trudinger–Moser inequality. Next, the existence of nonnegative solutions with negative energy is established by using Ekeland’s variational principle. The main feature of this paper consists in the presence of a (possibly degenerate) Kirchhoff model, combined with a critical Trudinger–Moser nonlinearity.
      PubDate: 2019-02-26
       
  • Geometric inequalities for hypersurfaces with nonnegative sectional
           curvature in hyperbolic space
    • Abstract: In this article, we will use inverse mean curvature flow to establish an optimal Sobolev-type inequality for hypersurfaces \(\Sigma \) with nonnegative sectional curvature in \(\mathbb {H}^n\) . As an application, we prove the hyperbolic Alexandrov–Fenchel inequalities for hypersurfaces with nonnegative sectional curvature in \(\mathbb {H}^n\) : $$\begin{aligned} \int _{\Sigma } p_{2k}\ge \omega _{n-1}\left[ \left( \frac{ \Sigma }{\omega _{n-1}}\right) ^\frac{1}{k} +\left( \frac{ \Sigma }{\omega _{n-1}}\right) ^{\frac{1}{k}\frac{n-1-2k}{n-1}}\right] ^k, \end{aligned}$$ where \(p_i\) is the normalized i-th mean curvature. Equality holds if and only if \(\Sigma \) is a geodesic sphere in \(\mathbb {H}^n\) . For a domain \(\Omega \subset \mathbb {H}^n\) with \(\Sigma =\partial \Omega \) having nonnegative sectional curvature, we prove an optimal inequality for quermassintegral in \(\mathbb {H}^n\) : $$\begin{aligned} W_{2k+1}(\Omega )\ge \frac{\omega _{n-1}}{n}\sum _{i=0}^{k}\frac{n-1-2k}{n-1-2i} C_k^i\left( \frac{ \Sigma }{\omega _{n-1}}\right) ^\frac{n-1-2i}{n-1}, \end{aligned}$$ where \(W_i(\Omega )\) is the i-th quermassintegral in integral geometry. Equality holds if and only if \(\Sigma \) is a geodesic sphere in \(\mathbb {H}^n\) . All these inequalities were previously proved by Ge et al. (J Differ Geom 98:237–260, 2014) under the stronger condition that \(\Sigma \) is horospherical convex.
      PubDate: 2019-02-23
       
 
 
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