preprint

Inserted: 4 jan 2021
Last Updated: 4 jan 2021

Journal: Trans. Amer. Math. Soc.
Volume: 365
Number: 9
Pages: 4699-4727
Year: 2013
Doi: 10.1090/S0002-9947-2013-05765-0

Abstract:

Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss the equivalence between the Lioville property and the Khas'minskii condition, i.e. the existence of an exhaustion functions which is also a supersolution for the operator outside a compact set. This generalizes a previous result obtained by one of the authors and answers to a question in "Aspects of potential theory, linear and nonlinear" by Pigola, Rigoli and Setti.