Inserted: 24 jul 2014
Last Updated: 29 aug 2015
Journal: Commun. Contemp. Math.
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