Optimal partial regularity for sub-elliptic systems with Dini continuous coefficients under the superquadratic natural growth. (February 2015)

• Record Type: Journal Article
• Authors: Wang, Jialin; Liao, Dongni; Gao, Shujing; Yu, Zefeng
• Is Part Of: Nonlinear analysis. Volume 114(2015)
• Page Start: 13
• Page End: 25
• Publication Date: 2015-02
• Subjects: 35H20 -- 35B65; Optimal partial regularity -- Heisenberg group -- Sub-elliptic system -- Dini continuity coefficient -- A-harmonic approximation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.10.028
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper is concerned with nonlinear sub-elliptic systems with Dini continuous coefficients under super-quadratic ( m > 2 ) natural growth conditions in the Heisenberg group. A general criterion for weak solutions to be regular in the neighborhood of a given point is established by a generalization of method of A -harmonic approximation. In particular, our result is optimal in the sense that in the case of Hölder continuous coefficients we obtain directly the optimal Hölder exponent for horizontal gradient of weak solutions on its regular set.