Wednesday 29 March 2017 h.14:30, Room 2BC30

Francesco Ferraresso (Padova, Dip. Mat.)

“An introduction to domain perturbation theory for elliptic eigenvalue problems”

Abstract

How does the sound of a drum depend on its shape? This weak variant of the classical question “Can one hear the shape of a drum?” can be considered in the framework of domain perturbation theory for elliptic differential operators. Starting with easy examples we will see that the answer to this apparently harmless question is rather different in the case of regular perturbations and in the case of singular perturbations. We will focus on the singular case, where the geometry of the problem is deeply mixed with the differential structure, in particular with the boundary conditions. Finally, we will give an account of recent advances in the study of a specific singular perturbation (the dumbbell domain) for the Laplace operator and for the biharmonic operator.

The seminar is intended for a general audience and it aims to introduce basic concepts from spectral theory as well as more advanced research results.