On the boundary of the attainable set of the Dirichlet spectrum

Lorenzo Brasco, Carlo Nitsch, Aldo Pratelli

Denoting by $\mathcal{E}\subseteq {\mathbb{R}}^2$ the set of the pairs $({\lambda }_1(\Omega ),{\lambda }_2(\Omega ))$ for all the open sets $\Omega \subseteq {\mathbb{R}}^N$ with unit measure, and by $\Theta \subseteq {\mathbb{R}}^N$ the union of two di…