Regularity for a Nonlinear Discontinuous Subelliptic System with Drift on the Heisenberg Group

Abstract

In this paper, we prove the partial Hölder regularity of weak solutions and the partial Morrey regularity to horizontal gradients of weak solutions to a nonlinear discontinuous subelliptic system with drift on the Heisenberg group by the $A$ -harmonic approximation, where the coefficients in the nonlinear subelliptic system are discontinuous and satisfy the VMO condition for $x$ , ellipticity and growth condition with the growth index $1<p<2$ for the Heisenberg gradient variable, and the nonhomogeneous terms satisfy the controllable growth condition and the natural growth condition, respectively.