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

Key Points

• Optimal partial Hölder continuity is achieved for weak solutions with mean oscillation coefficients, and exact exponents are determined.
• A new A-harmonic approximation reformulation leads the analysis, showing its effectiveness in handling bilinear forms under certain conditions.
• Discontinuous quasilinear sub-elliptic systems are explored, revealing the complexity and nuances tied to Hörmander’s vector fields.
• This research responds to the need for improved understanding of continuity in the context of weak solutions, expanding theoretical frameworks.