Lp-uniqueness for elliptic operators with unbounded coefficients in RN ✩

Let A be an elliptic operator with unbounded and sufficiently smooth coefficients and let μ be a (sub)- invariant measure of the operator A. In this paper we give sufficient conditions guaranteeing that the closure of the operator (A,C ∞ c (RN)) generates a sub-Markovian strongly continuous semigroup of contractions in Lp(RN,μ). Applications are given in the case when A is a generalized Schrödinger operator. © 2008 Elsevier Inc. All rights reserved