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

• Main Authors: Wang Jialin, Zhu Maochun, Gao Shujin, Liao Dongni
• Format: Article
• Language: English
• Published: De Gruyter 2020-08-01
• Series: Advances in Nonlinear Analysis
• Subjects: partial hölder continuity; heisenberg group; sub-quadratic controllable growth; sub-quadratic natural growth; vmo-coefficient; p-laplacian; 35h20; 35b65; 32a37
• Online Access: https://doi.org/10.1515/anona-2020-0145

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.