Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses

Pierre Bérard (1) , Bernard Helffer (2, 3)

1 IF - Institut Fourier
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 LMJL - Laboratoire de Mathématiques Jean Leray

In this paper, we revisit Courant's nodal domain theorem for theDirichlet eigenfunctions of a square membrane, and the analyses ofA. Stern and Å. Pleijel.

Mots clés: Nodal domains; Courant theorem; Nodal lines

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Pierre Bérard, Bernard Helffer. Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses. Springer Proceedings in Mathematics & Statistics, 2015, Analysis and Geometry. MIMS-GGTM conference in memory of M. S. Baouendi. Ali Baklouti, Aziz El Kacimi, Sadok Kallel, and Nordine Mir Editors., 127, pp.69--114. ⟨hal-00951531v4⟩