Sur un probleme d'optimisation de domaine

Let Ω be a bounded open subset of R ⁿ; with every measurable subset A of Ω is associated the real number En(A), related to capacity (for electrostatic problems) or to heat flux (for problems of thermal conduction). One investigates the minimization of En(A) when the measure of A is imposed. Penalty methods allows one to apply some techniques of convex analysis.