Partial regularity for discontinuous sub-elliptic systems with subquadratic growth in the Heisenberg group. (June 2020)

• Record Type: Journal Article
• Authors: Wang, Jialin; Zhang, Shuijin; Yang, Qiang; Liao, Dongni
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35H20 -- 35B65; Sub-quadratic growth -- VMO-coefficient -- Heisenberg group -- Partial Hölder continuity -- Nonlinear sub-elliptic system; 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.2019.111719
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group, and prove partial Hölder continuity for discontinuous sub-elliptic problems with subquadratic growth by a generalization of the technique of A -harmonic approximation. The model case is the sub-elliptic p -Laplace system with VMO-coefficients in the form − ∑ i = 1 2 n X i A i α ( ξ ) 1 + | X u | 2 p − 2 2 X i u α = 0, where A i α ( ξ ) ∈ V M O, and 1 < p < 2 .