Abstract : In the paper the support of a Radon measure is selected in an optimal way. The solution of the second order elliptic equation depends on the mesure via the mixed type boundary conditions. The existence of a solution for a class of domain optimization problems is shown. The relaxed formulation of the optimization problems is proposed. The first order necessary optimality conditions are derived.
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Antoine Henrot, Werner Horn, Jan Sokolowski. Domain Optimization Problem for Stationary Heat Equation. [Research Report] RR-2788, INRIA. 1996, pp.26. ⟨inria-00073903⟩