A note on the moving hyperplane method

TL;DR

This paper refines the understanding of the regularity conditions necessary for the moving hyperplane method to ensure monotonicity and symmetry in p-Laplace equations, focusing on the continuity properties of related parameters.

Contribution

It provides more precise regularity conditions and analyzes the continuity and semicontinuity of parameters involved in the moving hyperplane method for p-Laplace equations.

Findings

Enhanced regularity conditions for the moving hyperplane method.

Analysis of continuity and semicontinuity of key parameters.

Improved understanding of symmetry and monotonicity results.

Abstract

We give more precision on the regularity of the domain that is needed to have the monotonicity and symmetry results recently proved by Damascelli and Pacella, result concerning p-Laplace equations. For this purpose, we study the continuity and semicontinuity of some parameters linked with the moving hyperplane method.