Generalizations of Pleijel's nodal domain
GFM seminar
FCUL, C6, room 6.2.33
2017-04-04 14:00
2017-04-04 15:00
2017-04-04
14:00
..
15:00
by Corentin Léna (Università degli Studi di Torino)
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.