I am asking a question that I have already asked, but which did not have any success for the answers let $\lambda_{1}(\Omega),\lambda{2}(\Omega),\lambda_{3}(\Omega)...$ the eigenvlues of the laplacian Operator with Dirichlet condition on the boundary on $\Omega $
the classical spectrale optimisation problem is : $$ min\{\lambda_{k}(\Omega),\; \Omega\subset \mathbb{R}^N open ,\; |\Omega| = c\;\},$$ where $|.|$denoted the Lebesgue measure , $c>0$, $k \in \mathbb{N}^{\ast}$ and $\lambda_{k}$ is the $k-$eme eigenvalue of Dirichlet-lapalacian on $\Omega$.
I would like to know what is the application of this Problem (For the laplacian or another Operator) in the physics or the natural sciences..
thank you for your answers