Symmetry and monotonicity of singular solutions of double phase problems

TL;DR

This paper investigates positive singular solutions of PDEs from double phase functionals, establishing their symmetry and monotonicity using an advanced moving plane method.

Contribution

It introduces a novel application of the moving plane method to analyze symmetry and monotonicity of singular solutions in double phase problems.

Findings

Positive singular solutions exhibit symmetry.

Solutions are monotonic in certain directions.

The method can be applied to similar PDE problems.

Abstract

We consider positive singular solutions of PDEs arising from double phase functionals. Exploiting a rather new version of the moving plane method originally developed by Sciunzi, we prove symmetry and monotonicity properties of such solutions.