Corentin Léna
Università degli Studi di Torino

Abstract: Courant's nodal domain theorem tells us that an eigenfunction associated with the k^th eigenvalue of the Laplacian has at most k nodal domains. A. Pleijel showed in 1956 that for a given planar domain, eigenfunctions satisfying a Dirichlet boundary condition reach equality only for a finite number of k. We will study a generalization of this theorem to Robin-type boundary conditions, including the Neumann one, in any dimension. We will also consider the sharper results that can be obtained for particular domains.