Uniqueness in Weighted Lebesgue Spaces for an Elliptic Equation with Drift on Manifolds

Abstract

We investigate the uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of elliptic equations with a drift posed on a complete, noncompact, Riemannian manifold M of infinite volume and dimension Nge 2. Furthermore, in the special case of a model manifold with polynomial volume growth, we show that the conditions on the drift term are sharp.