Por Davide Zucco (Università di Torino).

Abstract: We discuss various shape optimization problems for the first eigenvalue of the Laplacian of a fixed bounded domain in the plane with Dirichlet boundary conditions. We impose the Dirichlet condition over a supplementary region, the obstacle (i.e., a compact set of possibly positive measure), which is the unknown in the optimization problem and is subjected to perimeter or area constraints. Then, we look for the best obstacle, both in shape and location, which optimizes this eigenvalue.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.