Regularity for sub-elliptic systems with VMO-coefficients in the Heisenberg group: the sub-quadratic structure case

Abstract

We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group. On the basis of a generalization of the technique of 𝓐-harmonic approximation introduced by Duzaar-Grotowski-Kronz, and an appropriate Sobolev-Poincaré type inequality established in the Heisenberg group, we prove partial Hölder continuity results for vector-valued solutions of discontinuous sub-elliptic problems. The primary model covered by our analysis is the non-degenerate sub-elliptic p-Laplacian system with VMO-coefficients, involving sub-quadratic growth terms.

Keywords

• partial hölder continuity
• heisenberg group
• sub-quadratic controllable growth
• sub-quadratic natural growth
• vmo-coefficient
• p-laplacian
• 35h20
• 35b65
• 32a37