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.
Citation: Beibei Chen, Jialin Wang, Dongni Liao. Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case[J]. AIMS Mathematics, 2025, 10(1): 1407-1437. doi: 10.3934/math.2025065
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.
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Beibei Chen, Jialin Wang, Dongni Liao. Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case[J]. AIMS Mathematics, 2025, 10(1): 1407-1437. doi: 10.3934/math.2025065
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