We consider the minimization of Dirichlet eigenvalues λk휆k , k∈Nk∈N , of the Laplacian on cuboids of unit measure in R3R3 . We prove that any sequence of optimal cuboids in R3R3 converges to a cube of unit measure in the sense of Hausdorff as k→∞k→∞ . We also obtain an upper bound for that rate of convergence.
- Spectral optimisation
- Dirichlet eigenvalues