Oberseminar "Mathematik des Maschinellen Lernens und Angewandte Analysis" - Prof. Dr. Roberto Ognibene

We consider the problem of the stability of eigenvalues of the Laplacian on a fixed bounded domain, under a perturbation consisting in removing a small set from the interior. The result strongly depends on which kind of 
boundary conditions are prescribed on the hole. In the talk, I will focus on three relevant instances: Dirichlet, Neumann and Robin boundary conditions. Our contribution (joint work with V. Felli and L. Liverani) concerns the 
Neumann case.