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This is a Quantitative Study study.

October 1, 2025

A variational method for functionals depending on eigenvalues

Key Points

Convergence results were established for Palais–Smale sequences related to eigenvalues.
Variational methods were adapted to apply to locally Lipschitz functionals and eigenvalue problems.
The methodology extends classical min-max methods for studying combinations of eigenvalues.
The analysis specifically focuses on Laplace and Steklov eigenvalues in dimensional settings.

Abstract

Abstract 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 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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Cite This Study

Romain Petrides (Tue,) studied this question.

synapsesocial.com/papers/68dd89e6fe798ba2fc498073 https://doi.org/https://doi.org/10.1112/jlms.70315

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