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

Mari, L., Valtorta, D. (2013). On the equivalence of stochastic completeness and liouville and Khas'minskii conditions in linear and nonlinear settings. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 365(9), 4699-4727 [10.1090/S0002-9947-2013-05765-0].

On the equivalence of stochastic completeness and liouville and Khas'minskii conditions in linear and nonlinear settings

Valtorta, D
2013

Abstract

Set in the Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, which in some sense are modeled after the p-Laplacian with potential. In particular, we discuss the equivalence between the Liouville property and the Khas'minskii condition, i.e. the existence of an exhaustion function which is also a supersolution for the operator outside a compact set. This generalizes a previous result obtained by one of the authors.
Articolo in rivista - Articolo scientifico
Khas'minskii condition; Parabolicity; Stochastic completeness;
English
2013
365
9
4699
4727
open
Mari, L., Valtorta, D. (2013). On the equivalence of stochastic completeness and liouville and Khas'minskii conditions in linear and nonlinear settings. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 365(9), 4699-4727 [10.1090/S0002-9947-2013-05765-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/393675
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