Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators
by Veronica Felli
Abstract: In this talk, I will first describe the sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then I will discuss some applications of this spectral stability to the study of the asymptotic behaviour of eigenvalues of Aharonov-Bohm operators
with two colliding poles. The talk is based on results obtained in collaboration with L. Abatangelo (Milano-Bicocca), C. LÃ©na (Torino) and L. Hillairet (OrlÃ©ans).