Ground state energy of the magnetic Laplacian on corner domains (Q2801549)

This paper devotes to studying the asymptotical behavior of the first eigenvalues of magnetic Laplacian associated to a large magnetic field, posed on a bounded 3-dimensional domain with Neumann boundary conditions. The authors considered the more general situations and provided a unified treatment of smooth corner domains. More precisely, the problematic of the large magnetic field for the magnetic Laplacian is equivalent to the semiclassical limit of the Schrödinger operator when the parameter \(h\) tends to 0. The semiclassical limit of the ground state energy is provided by the infimum of local energies defined at each point of the closure of the domain and local energies are ground state energies of adapted tangent operators at each point. The tangent operators which are obtained by freezing the magnetic field at each point acting on the tangent model domain. For corner domains, various infinite cones have to be added to the collection of tangent domains and this is different from smooth domains case. In the present work, they investigated the behavior of the local energy in general 3-dimensional corner domains and proved in particular that it attains its minimum. Some part of their results can also be extended to \(n\)-dimensional corner domains.