Special Session 7: Recent developments on nonlinear geometric PDEs

Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle
Gianmaria Verzini
Politecnico di Milano
Italy
Co-Author(s):    Benedetta Noris, Giovanni Siclari
Abstract:
We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains $\Omega$ having prescribed volume and contained in a fixed box $D$; equivalently, we look for the best way to remove a compact set (obstacle) $K\subset\overline{D}$ of Lebesgue measure $|K|=\varepsilon$, $0