# Maximization of the second Neumann eigenvalue: the general case

Published in *Pavillon André-Aisenstadt, room AA-5183*, 2018

In this talk we consider the second (non-trivial) eigenvalue $\mu_2(\Omega)$ of the Laplacian with Neumann boundary conditions. Using suitable test functions and a topological argument, we prove that $\mu_2(\Omega)$ is always less than $\mu_2(\Omega^*)$ where $\Omega^*$ is the ball of same volume as $\Omega$.

This is a joint work with Dorin Bucur (Chambery, France)