Optimal partial regularity of discontinuous subelliptic systems with VMO coefficients related to Hörmander’s vector fields

Abstract

Abstract In this paper, we study discontinuous subelliptic systems with VMO coefficients related to Hörmander’s vector fields. In the case of growth exponential p ≥ 2 $p\geq 2$ , the regularity results of the partial Hölder continuity of weak solutions are established based on the A $\mathcal{A}$ -harmonic approximation method under the controllable growth condition.

Keywords

• Hörmander’s vector fields
• Partial regularity
• Discontinuous subelliptic systems
• VMO coefficients
• A $\mathcal{A}$ -harmonic approximation technique