Calculus of Variations and Geometric Measure Theory

L. Brasco - C. Nitsch - C. Trombetti

An inequality à la Szego-Weinberger for the $p-$Laplacian on convex sets

created by brasco on 24 Jul 2014
modified on 29 Aug 2015


Accepted Paper

Inserted: 24 jul 2014
Last Updated: 29 aug 2015

Journal: Commun. Contemp. Math.
Pages: 22
Year: 2015


In this paper we prove a sharp upper bound for the first nontrivial eigenvalue of the $p-$Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants and extensions are investigated as well.

Keywords: shape optimization, Nonlinear eigenvalue problems