Abstract:We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form P (Ω)T q (Ω)|Ω| −2q−1/2 and the class of admissible domains consists of two-dimensional open sets Ω satisfying the topological constraints of having a prescribed number k of bounded connected components of the complementary set. A relaxed procedure is needed to have a well-posed problem and we show that when q < 1/2 an optimal relaxed d… Show more
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