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.
Borrelli, W., Mosconi, S., Squassina, M., Concavity properties for solutions to p-Laplace equations with concave nonlinearities, <<ADVANCES IN CALCULUS OF VARIATIONS>>, 2022; 0 (0): 1-19. [doi:10.1515/acv-2021-0100] [https://hdl.handle.net/10807/229409]
Concavity properties for solutions to p-Laplace equations with concave nonlinearities
Borrelli, William;Squassina, Marco
2022
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.