An overview on constrained critical points of Dirichlet integrals
Analysis of PDEs
2019-07-02 v1 Spectral Theory
Abstract
We consider a natural generalization of the eigenvalue problem for the Laplacian with homogeneous Dirichlet boundary conditions. This corresponds to look for the critical values of the Dirichlet integral, constrained to the unit sphere. We collect some results, present some counter-examples and compile a list of open problems.
Cite
@article{arxiv.1907.00882,
title = {An overview on constrained critical points of Dirichlet integrals},
author = {Lorenzo Brasco and Giovanni Franzina},
journal= {arXiv preprint arXiv:1907.00882},
year = {2019}
}
Comments
41 pages, 5 figures. This paper evolved from a set of notes for a talk delivered by the first author at the workshop "Nonlinear Meeting in Turin 2019"