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

William Borrelli, Sunra Mosconi, Marco Squassina

Published 2021-11-29, updated 2022-01-31Version 3

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.