2 problems

Let $\Omega$ be a bounded domain in $\mathbb{R}^2$, and let $\mathfrak L_k(\Omega)$ denote the infimum of the maximal first Dirichlet eigenvalue over all $k$-partitions of $\Omega$…

Let $\Omega$ be a bounded planar domain of area $A(\Omega)$, let $\mathfrak L_k(\Omega)$ denote the minimal energy of a $k$-partition of $\Omega$, and let $Hexa_1$ be the regular h…