Regularity results for quasilinear elliptic equations in the Heisenberg group

Abstract

We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group \({\mathbb{H}}^n\) . The model case is the non-degenerate p-Laplacean operator \(\sum_{i=1}^{2n} X_i \left( \left(\mu^2+ \left| {\mathfrak{X}}u \right|^2\right)^\frac{p-2}{2} X_i u\right) =0,\) where \(\mu > 0\) , and p is not too far from 2.