# Minimize Dirichlet eigenvalues for Laplace operator

Good time of day. Can you help me please?

I try to solve the following task for the Laplace operator for bounded domain $$\Omega \subset R^2$$ with Dirichlet eigenvalues.

I know that that the disc minimizes the first Dirichlet eigenvalue $$\lambda_1(\Omega)$$ among all planar domains of the same area. Also I know that the disjoint union of two discs of the same radius minimizes $$\lambda_2(\Omega)$$ among all planar domains of the same area (Faber-Krahn theorem).

I try to understand why that the disjoint union of $$n$$ discs of the same radius cannot minimize Dirichlet eigenvalues $$\lambda_n(\Omega)$$ for all $$n$$. I have found in this article (https://arxiv.org/abs/0808.2968v1) that this contradicts Weyl's law but I don't understand why it contradicts. Please help me and explain it in more detail.

Thank you