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

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 N≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 2$$\end{document}. Furthermore, in the special case of a model manifold with polynomial volume growth, we show that the conditions on the drift term are sharp.