Partial Hölder continuity for nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group

Abstract

We consider nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group and prove partial Hölder continuity results for weak solutions using a generalization of the technique of 𝒜{\mathcal{A}}-harmonic approximation. The model case is the following non-degenerate p-sub-Laplace system with super-quadratic natural growth with respect to the horizontal gradients Xu:

Keywords

• partial hölder continuity
• heisenberg group
• nonlinear sub-elliptic system
• vmo-coefficient
• super-quadratic natural growth
• 35h20
• 35b65