$C^{1,\alpha}$-Regularity of Quasilinear equations on the Heisenberg Group

TL;DR

This paper extends classical regularity results for quasilinear elliptic equations to the Heisenberg Group, covering a broad class of equations with various growth conditions, including polynomial and exponential types.

Contribution

It generalizes the $C^{1,eta}$ regularity theory to the setting of the Heisenberg Group for a wide class of quasilinear equations.

Findings

Established $C^{1,eta}$ regularity for equations with isotropic growth on the Heisenberg Group.

Included equations with polynomial and exponential growth conditions.

Extended classical regularity results to a non-commutative geometric setting.

Abstract

In this article, we reproduce results of classical regularity theory of quasilinear elliptic equations in the divergence form, in the setting of Heisenberg Group. The considered cases encompass a very wide class of equations with isotropic growth conditions that are generalizations of the $p$-Laplacian type equation and also include equations with polynomial or exponential type growth. Some more general conditions have also been explored.