Venue
Aula Magna
Abstract
We consider the first eigenvalue of the Dirichlet-Laplacian in a general open set. We seek for a geometric lower bounds, in terms of the inradius (i.e. the radius of a largest ball contained in the set). At first, we review some classical results, by focusing in particular on planar sets. We then present the natural counterparts of these results for the case of the fractional Dirichlet-Laplacian. We obtain estimates for open planar sets, in terms of their topology. The results obtained are sharp, in many respects.
Some of the results presented have been obtained in collaboration with Francesca Bianchi (Parma).
Some of the results presented have been obtained in collaboration with Francesca Bianchi (Parma).