Concave solutions to Finsler $p$-Laplace type equations

TL;DR

This paper establishes concavity properties for solutions to anisotropic quasi-linear equations, extending Euclidean results to nonsmooth and non-even anisotropies, broadening the understanding of these equations.

Contribution

It introduces new concavity results for anisotropic Finsler p-Laplace equations, including nonsmooth and non-even anisotropic functions, expanding previous Euclidean-based findings.

Findings

Proved concavity of solutions in anisotropic settings

Extended results to nonsmooth anisotropies

Allowed anisotropies to be non-even functions

Abstract

We prove concavity properties for solutions to anisotropic quasi-linear equations, extending previous results known in the Euclidean case. We focus the attention on nonsmooth anisotropies and in particular we also allow the functions describing the anisotropies to be not even.