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Research Article | Open Access

Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case

Beibei Chen, Jialin Wang( ), Dongni Liao( )
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
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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.

Keywords

gradient regularityDini continuous coefficientHeisenberg groupdrift termsub-quadratic growth
CLC number: 35B65, 35H20

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 1407-1437
DOI: 10.3934/math.2025065

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Cite this article:
Chen B, Wang J, Liao D. Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case. AIMS Mathematics, 2025, 10(1): 1407-1437. https://doi.org/10.3934/math.2025065

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Received: 05 November 2024
Revised: 09 January 2025
Accepted: 13 January 2025
Published: 15 January 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)