A Variational Characterisation of the Second Eigenvalue of the p-Laplacian on Quasi Open Sets

Abstract

In this article, we prove a minimax characterization of the second eigenvalue of the p-Laplacian operator on p-quasi-open sets, using a construction based on minimizing movements. This leads also to an existence theorem for spectral functionals depending on the first two eigenvalues of the p-Laplacian.

arXiv comment34 pages

References in corpus (1)

• A uniqueness result for functions with zero fine gradient on quasiconnected and finely connected sets

Cited by in corpus (4)

• Homological eigenvalues of graph $p$-Laplacians
• Optimization results for the higher eigenvalues of the $p$-Laplacian associated with sign-changing capacitary measures
• The Dirichlet problem for p-minimizers on finely open sets in metric spaces
• Convergence and local-to-global results for $p$-superminimizers on quasiopen sets