Inserted: 11 jun 2019
Last Updated: 11 jun 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