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

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.