The moving plane method for doubly singular elliptic equations involving a first order term

TL;DR

This paper extends the moving plane method to analyze symmetry and monotonicity of positive singular solutions in semilinear elliptic equations with a first order term and singular nonlinearity.

Contribution

It adapts the moving plane method to doubly singular elliptic equations with a first order term, establishing symmetry and monotonicity results.

Findings

Solutions exhibit symmetry and monotonicity properties.

The method effectively handles singular nonlinearities.

The approach broadens the applicability of the moving plane technique.

Abstract

In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov-Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.