Symmetry and monotonicity of singular solutions to $p$-Laplacian systems involving a first order term

TL;DR

This paper proves the symmetry of positive singular solutions to certain $p$-Laplacian PDE systems with a first order term, using an advanced moving plane method, extending known results even for scalar cases.

Contribution

It introduces a novel application of the moving plane method to establish symmetry of solutions in complex $p$-Laplacian systems with first order terms.

Findings

Symmetry of solutions is established for the PDE system.

The method applies to scalar cases as well.

New insights into singular solutions of $p$-Laplacian systems.

Abstract

We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by $p$-Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new version of the moving plane method, we prove the symmetry of the solutions. The result is already new in the scalar case.