Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators

[摘要] Maximum Principles on unbounded domains play a crucial role in several problems related to linear second-order PDEs of elliptic and parabolic type. In this paper we consider a class of sub-elliptic operators L in R-N and we establish some criteria for an unbounded open set to be a Maximum Principle set for L. We extend some classical results related to the Laplacian (by Deny, Hayman and Kennedy) and to the sub-Laplacians on stratified Lie groups (by Bonfiglioli and the second-named author). (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Maximum principle;Sub-elliptic operators;Homogeneous Hormander operators;Subharmonic and superharmonic functions