Calculus of Variations and Geometric Measure Theory
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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


Submitted Paper

Inserted: 30 nov 2021

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.

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