Eigenvalue inequalities for Schr'odinger operators on unbounded Lipschitz domains

摘要

Given a Schr\"odinger differential expression on an exterior Lipschitz domainwe prove strict inequalities between the eigenvalues of the correspondingselfadjoint operators subject to Dirichlet and Neumann or Dirichlet and mixedboundary conditions, respectively. Moreover, we prove a strict inequalitybetween the eigenvalues of two different elliptic differential operators on thesame domain with Dirichlet boundary conditions.