Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian p-Homogeneous Forms with a Potential in the Kato Class

Abstract

We define a notion of Kato class of measures relative to a Riemannian strongly local p-homogeneous Dirichlet form and we prove a Harnack inequality (on balls that are small enough) for the positive solutions to a Schrödinger-type problem relative to the form with a potential in the Kato class.