Seminario Dottorato: Shape optimization and polyharmonic operators

Wednesday 26 March 2014 h. 14:30, room 2BC30
Davide Buoso (Padova, Dip. Mat.)
"Shape optimization and polyharmonic operators"

Abstract
We will start by introducing the general shape optimization problem, giving motivations for its importance in applications.
Then we will turn to the problem of shape optimization for eigenvalues of elliptic operators (in particular, poyharmonic operators), which has regained popularity since 1993 with the paper by Buttazzo and Dal Maso. We will recall the most important classical results, giving the main ideas behind the proofs, together with the last ones.
Finally, we will move our attention to the problem of criticality with respect to shape deformations for eigenvalues of polyharmonic operators. After explaining the techniques involved, we will provide a characterization of criticality and show that balls are always critical.