A Free Boundary Optimization Problem
Andrew F. Acker · SIAM Journal on Mathematical Analysis · 1978
Given a convex set $Q \subset R^2 $ (bounded by a simple closed curve) and a constant $A > 0$, we determine the doubly-connected region $\Omega $ encircling (but not intersecting) Q, with area $| \Omega | \leqq A$, which has the least capacitance.