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 first eigenvalue equations. In the semilinear case p = 2 {p=2} the results are already new since they include new admissible nonlinearities.

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

William Borrelli;
2022-01-01

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 first eigenvalue equations. In the semilinear case p = 2 {p=2} the results are already new since they include new admissible nonlinearities.
2022
convexity of solutions
maximum principles
Quasilinear problems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1221290
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