Entire solutions of quasilinear elliptic systems on Carnot Groups

TL;DR

This paper establishes general a priori estimates for solutions of quasilinear elliptic systems on Carnot groups, leading to new non-existence results that are also novel in Euclidean spaces.

Contribution

It provides the first comprehensive a priori estimates and non-existence theorems for such systems on Carnot groups, extending known Euclidean results.

Findings

Derived new a priori estimates for solutions

Proved several non-existence theorems

Results are novel even in Euclidean space

Abstract

We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems. The results are new even in the Euclidean setting.