基于特征值的泛函变分方法

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-30 DOI:10.1112/jlms.70315

Romain Petrides

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引用次数: 0

摘要

给出了黎曼流形特征值泛函的系统变分方法。它基于palais - small （PS）序列的一个新概念，该概念可以通过将经典的C 1$ \mathcal {C}^1$泛函的最小-极大方法推广到局部Lipschitz泛函来构造。我们证明了由2维拉普拉斯特征值的组合或Steklov特征值的组合产生的这些PS序列的收敛性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A variational method for functionals depending on eigenvalues

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A variational method for functionals depending on eigenvalues

We perform a systematic variational method for functionals depending on eigenvalues of Riemannian manifolds. It is based on a new concept of Palais–Smale (PS) sequences that can be constructed thanks to a generalization of classical min-max methods on $C^{1}$ functionals to locally Lipschitz functionals. We prove convergence results on these PS sequences emerging from combinations of Laplace eigenvalues or combinations of Steklov eigenvalues in dimension 2.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.