Inserted: 19 jun 2018
Last Updated: 19 apr 2019
Journal: Proc. London Math. Soc.
In this article, we prove a minimax characterisation 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.