arXiv:1907.00882 Abstract | arXiv Analytics

arXiv:1907.00882 [math.AP]Abstract References Reviews Resources

An overview on constrained critical points of Dirichlet integrals

Published 2019-07-01Version 1

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.

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"

Categories: math.AP, math.SP

Subjects: 35P30, 49R05

Keywords: constrained critical points, dirichlet integral, homogeneous dirichlet boundary conditions, eigenvalue problem, open problems

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