Minimising Dirichlet eigenvalues on cuboids of unit measure

Abstract

We consider the minimisation of Dirichlet eigenvalues ${\lambda }_k$, $k\in \mathbb{N}$, of the Laplacian on cuboids of unit measure in ${\mathbb{R}}^3$. We prove that any sequence of optimal cuboids in ${\mathbb{R}}^3$ converges to a cube of unit measure in the sense of Hausdorff as $k\to \infty$.

11 pages

References in corpus (1)

• Extremal Eigenvalues of the Laplacian on Euclidean domains and closed surfaces