An overview on constrained critical points of Dirichlet integrals

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 $L^q$ sphere. We collect some results, present some counter-examples and compile a list of open problems.

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"

Cited by in corpus (1)

• On subhomogeneous indefinite $p$-Laplace equations in supercritical spectral interval