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- W3118710931 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 $P(Omega)T^q(Omega)|Omega|^{-2q-1/2}$ and the class of admissible domains consists of two-dimensional open sets $Omega$ 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 domain exists. When $q>1/2$ the problem is ill-posed and for $q=1/2$ the explicit value of the infimum is provided in the cases $k=0$ and $k=1$." @default.
- W3118710931 created "2021-01-18" @default.
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- W3118710931 date "2021-01-08" @default.
- W3118710931 modified "2023-10-16" @default.
- W3118710931 title "A shape optimization problem on planar sets with prescribed topology" @default.
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- W3118710931 doi "https://doi.org/10.48550/arxiv.2101.02886" @default.
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