Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case
Beibei Chen, Jialin Wang, Dongni Liao · AIMS Mathematics · 2025
This paper focuses on nonlinear sub-elliptic systems with drift terms in divergence form, under Dini continuity conditions, where the growth rate satisfies $ \frac{2Q}{Q+2} < m < 2 $, and $ Q $ represents the homogeneous dimension in the Heisenberg group. By generalizing the $ \mathcal{A} $-harmonic approximation technique to accommodate sub-quadratic growth, we establish the $ C^1 $ regularity associated with the horizontal gradient of weak solutions away from a negligible set.