Regularity of weak solution to discontinuous sub-elliptic systems with Orlicz growth on the Heisenberg group

Shengling Tu; Jialin Wang; Shuijin Zhang; Shengling Tu; Jialin Wang; Shuijin Zhang

doi:10.3934/math.2026948

AIMS Mathematics

2026, Volume 11, Issue 8: 23510-23550. doi: 10.3934/math.2026948

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Research article

Regularity of weak solution to discontinuous sub-elliptic systems with Orlicz growth on the Heisenberg group

School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China

Received: 20 May 2026 Revised: 20 July 2026 Accepted: 24 July 2026 Published: 03 August 2026
MSC : 35B65, 35H20

In this paper, we develop a unified approach for studying subelliptic systems with vanishing mean oscillation (VMO) discontinuous coefficients under Orlicz growth on the Heisenberg group, covering both the superquadratic and subquadratic cases. We establish an $ \mathcal{A} $-harmonic approximation adapted to the Orlicz growth framework on the Heisenberg group. Furthermore, assuming that the nonhomogeneous term satisfies a controllable growth condition, we obtain the partial Hölder regularity of weak solutions.
- Heisenberg group,
- Orlicz growth,
- VMO discontinuous coefficients,
- $ \mathcal{A} $-harmonic approximation,
- Hölder continuity
Citation: Shengling Tu, Jialin Wang, Shuijin Zhang. Regularity of weak solution to discontinuous sub-elliptic systems with Orlicz growth on the Heisenberg group[J]. AIMS Mathematics, 2026, 11(8): 23510-23550. doi: 10.3934/math.2026948

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Abstract

In this paper, we develop a unified approach for studying subelliptic systems with vanishing mean oscillation (VMO) discontinuous coefficients under Orlicz growth on the Heisenberg group, covering both the superquadratic and subquadratic cases. We establish an $ \mathcal{A} $-harmonic approximation adapted to the Orlicz growth framework on the Heisenberg group. Furthermore, assuming that the nonhomogeneous term satisfies a controllable growth condition, we obtain the partial Hölder regularity of weak solutions.

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