On Local Lipschitz Regularity For Quasilinear equations in the Heisenberg Group

TL;DR

This paper proves local Lipschitz continuity of weak solutions for a class of degenerated elliptic equations in the Heisenberg Group, extending results to more general quasilinear equations with polynomial or exponential growth.

Contribution

It establishes local Lipschitz regularity for solutions of degenerated elliptic equations in the Heisenberg Group under generalized growth conditions.

Findings

Proved local Lipschitz continuity of weak solutions.

Extended regularity results to equations with polynomial and exponential growth.

Generalized the classical p-Laplace equation to a broader class in the Heisenberg Group.

Abstract

The goal of this article is to establish local Lipschitz continuity of weak solutions for a class of degenerated elliptic equations of divergence form, in the Heisenberg Group. The considered hypothesis for the growth and ellipticity condition is a natural generalization of the p-Laplace equation and more general quasilinear elliptic equations with polynomial or exponential type growth.