The weak Pleijel theorem with geometric control

Pierre Bérard, Bernard Helffer

Let $\Omega \subset {\mathbb{R}}^d,d\ge 2$, be a bounded open set, and denote by $\lambda \_j(\Omega ),j\ge 1$, the eigenvalues of the Dirichlet Laplacian arranged in nondecreasing order, with mul…