Workshop Nosevol #3

Nicolas Popoff : Ground state energy of the magnetic Laplacian on general three-dimensional corner domains.

I will present recent results about the first eigenvalue of the magnetic Laplacian in general 3D-corner domains with Neumann boundary condition in the semi-classical limit. The use of singular chains show that the asymptotics of the first eigenvalue is governed by a hierarchy of model problems on the tangent cones of the domain. We provide estimates of the remainder depending on the geometry and the variations of the magnetic field.