Optimizing the first Dirichlet eigenvalue of the Laplacian with an obstacle
Optimizing the first Dirichlet eigenvalue of the Laplacian with an obstacle
Inside a fixed bounded domain $\Omega$ of the plane, we look for the best compact connected set $K$, of given perimeter, in order to maximize the first Dirichlet eigenvalue $\lambda_1(\Omega\setminus K)$. We discuss some of the qualitative properties of the maximizers, moving toward existence, regularity and geometry. Then we study …