On the existence and regularity of an optimal shape for the non-linear first eigenvalue problem with Dirichlet condition

We study a shape optimization problem associated with the first eigenvalue of a nonlinear spectral problem involving a mixed operator (p-Laplacian and Laplacian) with a constraint on the volume. First, we prove the existence of a quasi-open \Omega^*\subset D minimizer of the first eigenvalue under a volume constraint. Next, the... Show more