Weyl's law for Neumann Schrödinger operators on Hölder domains

Abstract

We review recent results on the semiclassical behaviour of Schrödinger operators with Neumann boundary conditions. In this setting, the validity of Weyl's law requires additional conditions on the potential. We will explain the techniques needed to control the number of bound states near the boundary, thus leading to universal estimates on the number of bound states.

References in corpus (2)

• Equivalence of Sobolev inequalities and Lieb-Thirring inequalities
• Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain