Continuity Properties of Covariant Schrödinger Semigroups

Abstract

Assume we are given a covariant Schrödinger operator $H_V^\nabla$ whose potential does not need to satisfy an $L^q_{loc}$ condition. A natural question to arise is under which assumptions all eigensections of this operator are automatically continuous. Note that under appropriate$L^q_{loc}$ conditions on V, one can use the local Sobolev embedding to deduce such continuity results.