2 problems

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…

Let $\Omega$ be a bounded planar domain, and let $\mathfrak L_k(\Omega)$ be the energy of a minimal $k$-partition of $\Omega$. Let $\hexagon$ be the regular hexagon of area $1$, an…