非局部 Neumann 问题的一般框架

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI:10.4310/cms.2024.v22.n1.a2

Guy Foghem, Moritz Kassmann

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引用次数: 20

摘要

在希尔伯特空间的框架内，我们解决了有界域中的非局部问题，并对域的补集规定了条件。我们的主要重点是在一个相当普遍的环境中解决非均质 Neumann 问题。我们还研究了从外部值问题到局部边界值问题的过渡。即使对于分数拉普拉斯算子，也有若干新结果。这一设置还涵盖了周动力学框架中的相关模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A general framework for nonlocal Neumann problems

Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also study the transition from exterior value problems to local boundary value problems. Several results are new even for the fractional Laplace operator. The setting also covers relevant models in the framework of peridynamics.

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来源期刊

Communications in Mathematical Sciences 数学-应用数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.