An inequality à la Szeg\H{o}-Weinberger for the $p-$Laplacian on convex sets

Lorenzo Brasco (1, 2) , Carlo Nitsch (3) , Cristina Trombetti (3)

1 I2M - Institut de Mathématiques de Marseille
2 DMCS - Dipartimento di Matematica e Informatica = Department of Mathematics and Computer Science [Ferrara]
3 Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”

In this paper we prove a sharp inequality of Szeg\H{o}-Weinberger type for the first nontrivial eigenvalue of the $p-$Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants, extensions and limit cases are investigated as well.

Mots clés: Nonlinear eigenvalue problems; shape optimization

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Lorenzo Brasco, Carlo Nitsch, Cristina Trombetti. An inequality à la Szeg\H{o}-Weinberger for the $p-$Laplacian on convex sets. Communications in Contemporary Mathematics, 2016, 18 (6), ⟨10.1142/S0219199715500868⟩. ⟨hal-01052624⟩