Partial regularity for discontinuous sub-elliptic systems with subquadratic growth in the Heisenberg group. (June 2020) - Wang, Jialin; Zhang, Shuijin; Yang, Qiang; Liao, Dongni
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 .