Calculus of Variations and Geometric Measure Theory

L. Brasco - G. Franzina

A note on positive eigenfunctions and hidden convexity

created by franzina on 06 Jun 2012
modified on 12 Feb 2013


Published Paper

Inserted: 6 jun 2012
Last Updated: 12 feb 2013

Journal: Arch. Math.
Pages: 7
Year: 2012


We give a simple convexity-based proof of the following fact: the only eigenfunction of the $p$−Laplacian that does not change sign is the first one. The method of proof covers as well more general nonlinear eigenvalue problems.

Keywords: Nonlinear eigenvalue problems, Uniqueness of eigenfunctions