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 the Dirichlet eigenfunctions of a square membrane and the analyses of A. Stern and Å. Pleijel.

Mots clés: Nodal lines; Nodal domains; Courant theorem

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

Pierre Bérard, Bernard Helffer. Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses. 2014. ⟨hal-00951531v2⟩