A nonvariational Neumann problem for the Helmholtz equation

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-11-27 DOI:10.1007/s10231-025-01614-8

Massimo Lanza de Cristoforis

引用次数: 0

Abstract

We consider a bounded open subset \(\Omega \) of \({\mathbb {R}}^n\) of class \(C^{1,\alpha }\) for some \(\alpha \in ]0,1[\) and we solve the Neumann problem for the Helmholtz equation both in \(\Omega \) and in the exterior of \(\Omega \). We look for solutions in the space of \(\alpha \)-Hölder continuous functions that may not have a classical normal derivative at the boundary points of \(\Omega \) and that may have an infinite Dirichlet integral around the boundary of \(\Omega \). Namely for solutions that do not belong to the classical variational setting.

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亥姆霍兹方程的非变分诺伊曼问题

我们考虑一个有界的开放子集\(\Omega \)的\({\mathbb {R}}^n\)类\(C^{1,\alpha }\)对于一些\(\alpha \in ]0,1[\)，我们解决了在\(\Omega \)和\(\Omega \)的外部亥姆霍兹方程的诺伊曼问题。我们在\(\alpha \) -Hölder连续函数的空间中寻找解，这些连续函数在\(\Omega \)的边界点上可能没有经典的正规导数，并且在\(\Omega \)的边界附近可能有一个无限的狄利克雷积分。即对于不属于经典变分设置的解。

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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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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