Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds

被引：0

作者：

Wang, Bing ^{[1
]}

Zhang, Hui-Chun ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, 135 Xingang Xi Rd, Guangzhou 510275, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2023年 / 285卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Liouville theorem; Sub-Laplacian; Generalized curvature-dimension; condition; Sub-Riemannian manifold; LIFE-SPAN; BLOW-UP; EQUATIONS; EXISTENCE; BEHAVIOR; VOLUME;

D O I：

10.1016/j.jfa.2023.110007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we generalize Liouville type theorems for some semilinear partial differential inequalities to sub-Riemannian manifolds satisfying a nonnegative generalized curvature -dimension inequality introduced by Baudoin and Garofalo in [5]. In particular, our results apply to all Sasakian manifolds with nonnegative horizontal Webster-Tanaka-Ricci curvature. The key ingredient is to construct a class of "good" cut-off functions. We also provide some upper bounds for lifespan to parabolic and hyperbolic inequalities. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：30

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