Abstract
AbstractWe 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 $$N\ge 2$$
N
≥
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.
Publisher
Springer Science and Business Media LLC
Reference30 articles.
1. Alias, L.J., Mastrolia, P., Rigoli, M.: Maximum principles and geometric applications. Springer Monographs in Mathematics. Springer International Publishing, Berlin (2016)
2. Aronson, D.G., Besala, P.: Uniqueness of solutions to the Cauchy problem for parabolic equations. J. Math. Anal. Appl. 13, 516–526 (1966)
3. Eidelman, S.D., Kamin, S., Porper, F.: Uniqueness of solutions of the Cauchy problem for parabolic equations degenerating at infinity. Asympt. Anal. 22, 349–358 (2000)
4. Gallot, S., Hulin, D., Lafontaine, J.: Riemannian Geometry, 2nd edn. Universitext. Springer, Berlin (1990)
5. Greene, R., Wu, H.H.: Function theory on manifolds which possess a pole. Lecture Notes in Mathematics, vol. 699. Springer, Berlin (1979)