与芬斯勒-拉普拉奇相关的超定问题

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-08-05 DOI:10.1112/mtk.12267

Antonio Greco, Benyam Mebrate

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引用次数: 0

摘要

本文考虑的是芬斯勒-拉普拉斯扭转方程。问题域由一个支持诺伊曼条件的圆锥面和一个同时支持迪里希特条件和诺伊曼条件的未知面限定。其中包括锥面与穿刺空间重合的情况。我们证明，弱解的存在意味着未知曲面位于芬斯勒球的边界上。顺便提一下，在温和的光滑性假设下，Finsler-Minkowski 准则的一些性质也在这里得到了证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

An overdetermined problem related to the Finsler -Laplacian

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An overdetermined problem related to the Finsler -Laplacian

In this paper, we consider the Finsler -Laplacian torsion equation. The domain of the problem is bounded by a conical surface supporting a Neumann-type condition, and an unknown surface supporting both a Dirichlet and a Neumann condition. The case when the cone coincides with the punctured space is included. We show that the existence of a weak solution implies that the unknown surface lies on the boundary of a Finsler-ball. Incidentally, some properties of the Finsler–Minkowski norms are proved here under mild smoothness assumptions.

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.