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 / Borrelli, W., Mosconi, S., Squassina, M.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 17:1(2024), pp. 79-97. [10.1515/acv-2021-0100]
Concavity properties for solutions to p-Laplace equations with concave nonlinearities
William Borrelli;
2024
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.| File | Dimensione | Formato | |
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