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.