Dirichlet parabolicity and L1-Liouville property under localized geometric conditions

• Published in: Journal of functional analysis Vol. 273; no. 2; pp. 652 - 693
• Main Authors: Pessoa, Leandro F., Pigola, Stefano, Setti, Alberto G.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.07.2017
• Subjects: [formula omitted]-Liouville property; Dirichlet parabolicity; Manifolds with boundary; L1-Liouville property; Dirichlet parabolicity; Manifolds with boundary

We shed a new light on the L1-Liouville property for positive, superharmonic functions by providing many evidences that its validity relies on geometric conditions localized on large enough portions of the space. We also present examples in any dimension showing that the L1-Liouville property is str...