Calculus of Variations and Geometric Measure Theory

W. Borrelli - S. J. N. Mosconi - M. Squassina

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

created by borrelli on 30 Nov 2021
modified on 22 Jul 2022


Published Paper

Inserted: 30 nov 2021
Last Updated: 22 jul 2022

Journal: Adv. Calc. Var.
Year: 2021

ArXiv: 2111.14801 PDF


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.