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Partial regularity for discontinuous sub-elliptic systems with VMO-coefficients involving controllable growth terms in Heisenberg groups. (English) Zbl 1404.35116

Summary: In this paper, we consider discontinuous sub-elliptic systems with VMO-coefficients for the controllable growth case of \(p \geq 2\) in the Heisenberg group. Based on a generalization of the technique of \(\mathcal{A}\)-harmonic approximation with the superquadratic growth case, a partial Hölder continuity result for weak solutions of discontinuous sub-elliptic systems with VMO-coefficients is established. In particular, the primary model covered by our analysis is the non-degenerate \(p\)-sub-Laplace system involving super-quadratic controllable growth terms.

MSC:

35H20 Subelliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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