The anisotropic p-capacity and the anisotropic Minkowski inequality

作     者：Chao Xia Jiabin Yin Chao Xia;Jiabin Yin

作者机构：School of Mathematical SciencesXiamen UniversityXiamen 361005China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第3期

页      面：559-582页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11871406)。 

主　　题：Minkowski inequality anisotropic mean curvature anisotropic p-Laplacian nonlinear potential theory p-capacity 

摘      要：In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total L^(p)anisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in R^(n).As consequences,we obtain an anisotropic Willmore inequality,a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality.For the proof,we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al.(2019).