Calculus of Variations and Geometric Measure Theory

G. Meglioli - A. Roncoroni

Uniqueness in weighted Lebesgue spaces for an elliptic equation with drift on manifolds

created by roncoroni on 13 Oct 2022
modified on 29 May 2024


Published Paper

Inserted: 13 oct 2022
Last Updated: 29 may 2024

Journal: J. Geom. Anal.
Volume: 33
Number: 320
Year: 2023

ArXiv: 2210.06275 PDF


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 $N\ge2$. Furthermore, in the special case of a model manifold with polynomial volume growth, we show that the conditions on the drift term are sharp.