Séminaire OrléansSharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles
Thursday 22 June 2017 14:00 - Orléans - Salle de Séminaire
In this talk I will briefly introduce the magnetic Schrodinger operator, the Aharonov-Bohm effect, and the associated eigenvalue problem. I will consider the special case of an operator with half-integer circulation, in a bounded planar domain, with homogeneous Dirichlet boundary conditions. I will present a result in collaboration with L. Abatangelo, V. Felli and M. Nys. We establish a sharp relation between the rate of convergence of the eigenvalues as the singular pole is approaching a point on the boundary of the domain and the number of nodal lines of the eigenfunction of the limiting problem ending at that point.