Calculus of Variations and Partial Differential Equations最新文献_第5页

A strong form of the quantitative Wulff inequality for crystalline norms 晶体规范的定量伍尔夫不等式的强形式

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-13 DOI: 10.1007/s00526-024-02796-4

Kenneth DeMason

引用次数: 0

On the Neumann (p, q)-eigenvalue problem in Hölder singular domains 论荷尔德奇异域中的诺依曼（p，q）特征值问题

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-10 DOI: 10.1007/s00526-024-02788-4

Prashanta Garain, Valerii Pchelintsev, Alexander Ukhlov

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BV estimates on the transport density with Dirichlet region on the boundary 边界上有德里赫特区域的传输密度 BV 估计值

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-10 DOI: 10.1007/s00526-024-02746-0

Samer Dweik

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Phase transition of an anisotropic Ginzburg–Landau equation 各向异性金兹堡-朗道方程的相变

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-10 DOI: 10.1007/s00526-024-02779-5

Yuning Liu

引用次数: 0

Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities 具有导数非线性的非线性薛定谔方程系统的变量问题

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-10 DOI: 10.1007/s00526-024-02782-w

Hiroyuki Hirayama, Masahiro Ikeda

引用次数: 0

Higher Robin eigenvalues for the p-Laplacian operator as p approaches 1 当 p 接近 1 时 p 拉普拉斯算子的高罗宾特征值

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-09 DOI: 10.1007/s00526-024-02769-7

José C. Sabina de Lis, Sergio Segura de León

{"title":"Higher Robin eigenvalues for the p-Laplacian operator as p approaches 1","authors":"José C. Sabina de Lis, Sergio Segura de León","doi":"10.1007/s00526-024-02769-7","DOIUrl":"https://doi.org/10.1007/s00526-024-02769-7","url":null,"abstract":"This work addresses several aspects of the dependence on p of the higher eigenvalues (lambda _n) to the Robin problem,\u0000$$begin{aligned} {left{ begin{array}{ll} -Delta _p u = lambda |u|^{p-2}u &{} qquad xin Omega , |nabla u|^{p-2}dfrac{partial u}{partial nu }+ b |u|^{p-2}u= 0&{}qquad xin partial Omega . end{array}right. } end{aligned}$$Here, (Omega subset {{mathbb {R}}}^N) is a (C^1) bounded domain, (nu ) is the outer unit normal, (Delta _p u = text {div} (|nabla u|^{p-2}nabla u)) stands for the p-Laplacian operator and (bin L^infty (partial Omega )). Main results concern: (a) the existence of the limits of (lambda _n) as (prightarrow 1), (b) the ‘limit problems’ satisfied by the ‘limit eigenpairs’, (c) the continuous dependence of (lambda _n) on p when (1 and (d) the limit profile of the eigenfunctions as (prightarrow 1). The latter study is performed in the one dimensional and radially symmetric cases. Corresponding properties on the Dirichlet and Neumann eigenvalues are also studied in these two special scenarios.","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":"33 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces 局部尤多维奇空间中欧拉流的存在性和唯一性的基本证明

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-05 DOI: 10.1007/s00526-024-02750-4

Gianluca Crippa, Giorgio Stefani

{"title":"An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces","authors":"Gianluca Crippa, Giorgio Stefani","doi":"10.1007/s00526-024-02750-4","DOIUrl":"https://doi.org/10.1007/s00526-024-02750-4","url":null,"abstract":"We revisit Yudovich’s well-posedness result for the 2-dimensional Euler equations for an inviscid incompressible fluid on either a sufficiently regular (not necessarily bounded) open set (Omega subset mathbb {R}^2) or on the torus (Omega =mathbb {T}^2). We construct global-in-time weak solutions with vorticity in (L^1cap L^p_{ul}) and in (L^1cap Y^Theta _{ul}), where (L^p_{ul}) and (Y^Theta _{ul}) are suitable uniformly-localized versions of the Lebesgue space (L^p) and of the Yudovich space (Y^Theta ) respectively, with no condition at infinity for the growth function (Theta ). We also provide an explicit modulus of continuity for the velocity depending on the growth function (Theta ). We prove uniqueness of weak solutions in (L^1cap Y^Theta _{ul}) under the assumption that (Theta ) grows moderately at infinity. In contrast to Yudovich’s energy method, we employ a Lagrangian strategy to show uniqueness. Our entire argument relies on elementary real-variable techniques, with no use of either Sobolev spaces, Calderón–Zygmund theory or Littlewood–Paley decomposition, and actually applies not only to the Biot–Savart law, but also to more general operators whose kernels obey some natural structural assumptions.","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":"86 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Well-posedness for Hamilton–Jacobi equations on the Wasserstein space on graphs 图上瓦瑟斯坦空间的汉密尔顿-雅可比方程的好求性

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-04 DOI: 10.1007/s00526-024-02758-w

Wilfrid Gangbo, Chenchen Mou, Andrzej Święch

引用次数: 0

A maximum rank theorem for solutions to the homogenous complex Monge–Ampère equation in a $$mathbb {C}$$ -convex ring $$mathbb{C}$$-凸环中同源复蒙日-安培方程解的最大秩定理

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-04 DOI: 10.1007/s00526-024-02764-y

Jingchen Hu

引用次数: 0

Morse index of concentrated solutions for the nonlinear Schrödinger equation with a very degenerate potential 具有非常退化势能的非线性薛定谔方程集中解的莫尔斯指数

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-04 DOI: 10.1007/s00526-024-02766-w

Peng Luo, Kefan Pan, Shuangjie Peng

{"title":"Morse index of concentrated solutions for the nonlinear Schrödinger equation with a very degenerate potential","authors":"Peng Luo, Kefan Pan, Shuangjie Peng","doi":"10.1007/s00526-024-02766-w","DOIUrl":"https://doi.org/10.1007/s00526-024-02766-w","url":null,"abstract":"We revisit the following nonlinear Schrödinger equation $$begin{aligned} -varepsilon ^2Delta u+ V(x)u=u^{p},quad u>0,;; uin H^1({mathbb {R}}^N), end{aligned}$$where (varepsilon >0) is a small parameter, (Nge 2) and (1<p<2^*-1). It is known that the Morse index gives a strong qualitative information on the solutions, such as non-degeneracy, uniqueness, symmetries, singularities as well as classifying solutions. Here we compute the Morse index of positive k-peak solutions to above problem when the critical points of V(x) are non-isolated and degenerate. We also give a specific formula for the Morse index of k-peak solutions when the critical point set of V(x) is a low-dimensional ellipsoid. Our main difficulty comes from the non-uniform degeneracy of potential V(x). Our results generalize Grossi and Servadei’s work (Ann Math Pura Appl 186: 433–453, (2007)) to very degenerate (non-admissible) potentials and show that the structure of potentials highly affects the properties of concentrated solutions.","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":"38 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0