The nonlocal Neumann problem

IF 2.4 2区 数学 Q1 MATHEMATICS
Leonhard Frerick, Christian Vollmann, Michael Vu
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引用次数: 0

Abstract

The classical local Neumann problem is well studied and solutions of this problem lie, in general, in a Sobolev space. In this work, we focus on nonlocal Neumann problems with measurable, nonnegative kernels, whose solutions require less regularity assumptions. For kernels of this kind we formulate and study the weak formulation of the nonlocal Neumann problem and we investigate a nonlocal counterpart of the Sobolev space H1 as well as a resulting nonlocal trace space. We further establish, mainly for symmetric kernels, various existence results for the weak solution of the Neumann problem and we discuss related necessary conditions. Both, homogeneous and nonhomogeneous Neumann boundary conditions are considered.
非局部诺伊曼问题
经典局部诺伊曼问题得到了很好的研究,该问题的解一般存在于Sobolev空间中。在这项工作中,我们关注具有可测量的非负核的非局部诺伊曼问题,其解决需要较少的正则性假设。对于这类核,我们提出并研究了非局部Neumann问题的弱形式,并研究了Sobolev空间H1的非局部对应物以及由此产生的非局部迹空间。进一步建立了主要针对对称核的Neumann问题弱解的各种存在性结果,并讨论了相关的必要条件。同时考虑了齐次和非齐次诺依曼边界条件。
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
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