Concavity properties for solutions to $p$-Laplace equations with concave nonlinearities

TL;DR

This paper establishes new concavity properties for solutions to p-Laplace equations with concave nonlinearities, extending previous results to more general nonlinearities and including the semilinear case.

Contribution

It introduces novel concavity results for a broad class of quasi-linear equations involving the p-Laplace operator, generalizing prior findings to new nonlinearities.

Findings

New concavity results for p-Laplace equations with concave nonlinearities

Extension of known results to more general nonlinearities including the semilinear case

Solutions exhibit concavity properties up to a suitable transformation

Abstract

We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the $p$-Laplace operator and a general nonlinearity satisfying concavity type assumptions. This provides an extension of results previously known in the literature only for the torsion and the eigenfunction equations. In the semilinear case $p = 2$ the results are already new since they include new admissible nonlinearities.