Local Second Order Sobolev Regularity for p-Laplacian Equation in Semi-Simple Lie Group

被引：1

作者：

Yu, Chengwei ^{[1
]}

Zeng, Yue ^{[2
]}

机构：

[1] China Fire & Rescue Inst, Dept Basic, 4 Nanyan Rd, Beijing 102202, Peoples R China

[2] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

来源：

MATHEMATICS | 2024年 / 12卷 / 04期

基金：

中国国家自然科学基金;

关键词：

structural inequality; W-2; W-2-regularity; weak solutions; p-Laplacian equation; semi-simple Lie group; range of p; HARMONIC FUNCTIONS; C-1; C-ALPHA-REGULARITY;

D O I：

10.3390/math12040601

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a structural inequality of the infinity-subLaplacian Delta(0,infinity )in a class of the semi-simple Lie group endowed with the horizontal vector fields X-1,. . .,X-2n. When 1 < p <= 4 with n = 1 and 1 < p < 3 + 1/n-1 with n >= 2, we apply the structural inequality to obtain the local horizontal W-2,W- 2-regularity of weak solutions top-Laplacian equation in the semi-simple Lie group. Compared to Euclidean spaces R(2n )with n >= 2, the range of this p obtained is already optimal.

引用

页数：14

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