2 problems

Let $[\gamma_{ij}]$ satisfy the conditions in Theorem and have nullity $1$, with $\gamma>0$ its overall factor, so that $[\gamma_{ij}]/\gamma$ is fixed. Let $\vec u(\cdot;\gamma)$…

Choksi's ball-or-two-balls conjecture. Minimizers of the problem with uniform charge density are balls, unless it is better to split one ball into two equal-size balls.