Partial interior regularity for sub-elliptic systems with Dini continuous coefficients in Carnot groups: the sub-quadratic controllable case

被引：0

作者：

Liao, Dongni ^{[1
]}

Wang, Jialin ^{[1
]}

Yang, Qiang ^{[1
]}

Wu, Shimin ^{[2
]}

机构：

[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Jiangxi, Peoples R China

[2] Gannan Normal Univ, Sch Phys & Elect Informat Technol, Ganzhou 341000, Jiangxi, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2017年

基金：

中国国家自然科学基金;

关键词：

nonlinear sub-elliptic system; Dini continuous coefficients; sub-quadratic controllable growth; optimal partial regularity; Carnot groups; HARMONIC APPROXIMATION; MINIMIZERS; EQUATIONS; GROWTH; INTEGRALS;

D O I：

10.1186/s13661-017-0882-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider nonlinear sub-elliptic systems with Dini continuous coefficients for the case 1 < m < 2 in Carnot groups and prove a C-1-partial regularity result for weak solutions under the controllable growth conditions. Our method of proof for sub-elliptic systems is based on a generalization of the technique of A-harmonic approximation. It is interesting to point out that our result is optimal in the sense that in the case of Holder continuous coefficients we get directly the optimal Hlder exponent on its regular set.

引用

页数：24