Partial regularity for discontinuous sub-elliptic systems with subquadratic growth in the Heisenberg group (Q2309296)

The aim of the authors is to study nonlinear sub-elliptic systems with coefficients, belonging to the vanishing Mean Oscillation class (VMO), in the Heisenberg group. They 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 a suitable sub-elliptic $p$-Laplace system systems in divergence form with VMO-coefficients. The main new aspect of this paper is the fact that the authors are able to deal with the sub-quadratic growth $1 < p < 2 $ with respect to horizontal gradients and coefficients to be discontinuous. The method of proof employed is to avoid the use of $L^q-L^p$ estimates for the horizontal gradient and reverse Hölder inequalities.