Simon Stadler: Eigenvalue inequalities for partial differential operators

Abstract: We discuss eigenvalue inequalities for elliptic partial differential operators in two different settings. Given a Schrödinger differential expression on an unbounded Lipschitz domain with compact boundary we prove strict inequalities bewteen the eigenvalues of the corresponding selfadjoint operators subject to Dirichlet and Neumann or Dirichlet and Robin boundary conditions, respectively. Moreover, on a given domain we prove a strict inequality between the eigenvalues of two different elliptic differential operators subject to Dirichlet boundary conditions.

This talk is based on a joint work with Jussi Behrndt and Jonathan Rohleder.