Schrodinger equations with very singular potentials in Lipschitz domains

Abstract

Consider operators Lin Ω and also a second condition that guarantees the existence of a ground state Φ V . If, for example, V > 0 this condition reads 1 < c H (V ) (= the Hardy constant relative to V ). We derive estimates of positive L V harmonic functions and of positive Green potentials of measures τ ∈ M + (Ω; Φ V ). These imply estimates of positive L V superharmonic functions and of L V subharmonic functions that are dominated by an L V superharmonic. Similar results have been obtained in [7] in the case of smooth domains.