@article{Chen2025, 
author = {Beibei Chen and Jialin Wang and Dongni Liao},
title = {Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1407-1437},
keywords = {Heisenberg group, gradient regularity, Dini continuous coefficient, drift term, sub-quadratic growth},
url = {https://www.sciopen.com/article/10.3934/math.2025065},
doi = {10.3934/math.2025065},
abstract = {This paper focuses on nonlinear sub-elliptic systems with drift terms in divergence form, under Dini continuity conditions, where the growth rate satisfies              2      Q              Q      +      2        <  m  <  2, and    Q represents the homogeneous dimension in the Heisenberg group. By generalizing the        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.}
}