Optimal Shape for Elliptic Problems with Random Perturbations
نویسندگان
چکیده
In this paper we analyze the relaxed form of a shape optimization problem with state equation { − div ( a(x)Du ) = f in D boundary conditions on ∂D. The new fact is that the term f is only known up to a random perturbation ξ(x, ω). The goal is to find an optimal coefficient a(x), fulfilling the usual constraints α ≤ a ≤ β and ∫ D a(x) dx ≤ m, which minimizes a cost function of the form
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