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Article

Optimal Hölder Regularity for Discontinuous Sub-Elliptic Systems Structured on Hörmander’s Vector Fields

by
Dongni Liao
and
Jialin Wang
*
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(10), 761; https://doi.org/10.3390/axioms14100761 (registering DOI)
Submission received: 13 July 2025 / Revised: 1 October 2025 / Accepted: 9 October 2025 / Published: 12 October 2025
Versions Notes

Abstract

This paper studies discontinuous quasilinear sub-elliptic systems associated with Hörmander’s vector fields under controllable and natural growth conditions. By a new A-harmonic approximation reformulation for bilinear forms A∈Bil(RkN,RkN), we obtain optimal partial Hölder continuity with exact exponents for weak solutions with vanishing mean oscillation coefficients.
Keywords: Hörmander’s vector fields; partial Hölder continuity; quasi-linear sub-elliptic systems; A-harmonic approximation Hörmander’s vector fields; partial Hölder continuity; quasi-linear sub-elliptic systems; A-harmonic approximation

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MDPI and ACS Style

Liao, D.; Wang, J. Optimal Hölder Regularity for Discontinuous Sub-Elliptic Systems Structured on Hörmander’s Vector Fields. Axioms 2025, 14, 761. https://doi.org/10.3390/axioms14100761

AMA Style

Liao D, Wang J. Optimal Hölder Regularity for Discontinuous Sub-Elliptic Systems Structured on Hörmander’s Vector Fields. Axioms. 2025; 14(10):761. https://doi.org/10.3390/axioms14100761

Chicago/Turabian Style

Liao, Dongni, and Jialin Wang. 2025. "Optimal Hölder Regularity for Discontinuous Sub-Elliptic Systems Structured on Hörmander’s Vector Fields" Axioms 14, no. 10: 761. https://doi.org/10.3390/axioms14100761

APA Style

Liao, D., & Wang, J. (2025). Optimal Hölder Regularity for Discontinuous Sub-Elliptic Systems Structured on Hörmander’s Vector Fields. Axioms, 14(10), 761. https://doi.org/10.3390/axioms14100761

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