Moscow Mathematical Journal

Volume 15, Issue 4, October–December 2015 pp. 767–775.

Maximization of Higher Order Eigenvalues and Applications

Authors: Nikolai Nadirashvili (1) and Yannick Sire (2)
Author institution:(1) CNRS, I2M UMR 7353 – Centre de Mathématiques et Informatique, Marseille, France
(2) Université Aix-Marseille, I2M UMR 7353 – Centre de Mathématiques et Informatique, Marseille, France

Summary:

The present paper is a follow up of our paper “Conformal spectrum and harmonic maps”. We investigate here the maximization of higher order eigenvalues in a conformal class on a smooth compact boundaryless Riemannian surface. Contrary to the case of the first nontrivial eigenvalue as shown in the above-mentioned paper, bubbling phenomena appear.

2010 Math. Subj. Class. 35P15.

Keywords: Eigenvalues, isoperimetric inequalities.

Contents Full-Text PDF