Liouville-type results for some quasilinear anisotropic elliptic equations

TL;DR

This paper establishes Liouville-type theorems for stable solutions of quasilinear anisotropic elliptic equations, including the Finsler p-Laplacian, extending understanding of solution behavior in these complex systems.

Contribution

It provides new Liouville-type results for stable solutions of anisotropic elliptic equations, encompassing the Finsler p-Laplacian, which was not previously addressed.

Findings

Liouville-type theorems for stable solutions

Results cover solutions stable outside compact sets

Includes the case of Finsler p-Laplacian

Abstract

We prove some Liouville-type theorems for stable solutions (and solutions stable outside a compact set) of quasilinear anisotropic elliptic equations. Our results cover the particular case of the pure Finsler p-Laplacian.