Maximization and minimization of the principal eigenvalue of the Laplacian with indefinite weight under Dirichlet and Robin boundary conditions on classes of rearrangements

Claudia Anedda, Fabrizio Cuccu

Let $\Omega \subset {\mathbb{R}}^N$, $N\ge 1$, be a bounded connected open set. We consider the weighted eigenvalue problem $-\Delta u=\lambda mu$ in $\Omega$ with $\lambda \in \mathbb{R}$, $m\in L^{\infty }(\Omega )$ an…