Calculus of Variations and Geometric Measure Theory

L. Brasco - G. Franzina

An overview on constrained critical points of Dirichlet integrals

created by brasco on 11 Jun 2019
modified on 14 Oct 2019


Accepted Paper

Inserted: 11 jun 2019
Last Updated: 14 oct 2019

Journal: Rendiconti Sem. Mat. Univ. Pol. Torino
Pages: 42
Year: 2019


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.

Keywords: eigenvalues, Lane-Emden equation, constrained critical points