Optimization of the principal eigenvalue of the Neumann Laplacian with indefinite weight and monotonicity of minimizers in cylinders

Claudia Anedda, Fabrizio Cuccu

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