Prescription du spectre de steklov dans une classe conforme

Abstract

On any compact manifold of dimension n≥3 with boundary, we prescribe any finite part of the Steklov spectrum within a given conformal class. In particular, we prescribe the multiplicity of the first eigenvalues. On a compact surface with boundary, we show that the multiplicity of the k-th eigenvalue is bounded independently of the metric. On the disk, we give more precise results: the multiplicity of the first and second positive eigenvalues are at most 2 and 3 respectively. For the Steklov-Neumann problem on the disk, we prove that the multiplicity of the k-th positive eigenvalue is at most k+1. © 2014 Mathematical Sciences Publishers.