A variational method for functionals depending on eigenvalues
Analysis of PDEs
2024-10-11 v2 Differential Geometry
Functional Analysis
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 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 Palais-Smale sequences emerging from combinations of Laplace eigenvalues or combinations of Steklov eigenvalues in dimension 2.
Cite
@article{arxiv.2211.15632,
title = {A variational method for functionals depending on eigenvalues},
author = {Romain Petrides},
journal= {arXiv preprint arXiv:2211.15632},
year = {2024}
}