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

TL;DR

This paper provides a variational characterization of the second eigenvalue of the p-Laplacian on p-quasi-open sets, using minimax methods, and establishes an existence theorem for related spectral functionals.

Contribution

It introduces a new minimax variational approach for the second eigenvalue of the p-Laplacian on p-quasi-open sets, expanding spectral theory tools.

Findings

Minimax characterization of the second eigenvalue

Existence theorem for spectral functionals involving first two eigenvalues

Application of minimizing movements in spectral analysis

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.