Wolff potentials and regularity of solutions to integral systems on spaces of homogeneous type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Xiao, Yayuan¹ 

[1] Ball State Univ, Dept Math Sci, Muncie, IN 47306 USA

关键词: Wolff potentials;    Riesz potentials;    Spaces of homogeneous type;    Hardy-Littlewood-Sobolev type inequality;    Lane-Emden type integral system;    Integrability intervals;   

DOI  :  10.1016/j.jmaa.2018.12.006

来源: Elsevier

【 摘 要 】

Two objectives are accomplished in this paper: First we establish the comparison between Wolff and Riesz potentials on space of homogeneous type in the sense of Coifman and Weiss (Theorem 1.2), followed by a Hardy-Littlewood-Sobolev type inequality for Wolff potentials (Theorem 1.3). Then applying this inequality, we consider a Lane-Emden type integral system and use regularity lifting to derive integrability estimates of positive solutions to the system, by which we also imply L-infinity estimates (see Theorem 1.4 and 1.5). Furthermore, we use a modified regularity lifting method to prove that the positive solutions are also Lipschitz continuous (Theorem 1.6). Our results imply Wolff potentials and regularity of solutions to the Lane-Emden type integral systems on stratified groups and the Carnot-Carathedory metric spaces defined by a family of vector fields satisfying Hormander's finite rank condition as special cases. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free