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- W4285703977 abstract "In this paper we consider the functional begin{equation*} E_{p,la}(Omega):=int_Omega dist^p(x,pd Omega )d x+la frac{H^1(pd Omega)}{H^2(Omega)}. end{equation*} Here $pgeq 1$, $la>0$ are given parameters, the unknown $Omega$ varies among compact, convex, Hausdorff two-dimensional sets of $R^2$, $pd Omega$ denotes the boundary of $Omega$, and $dist(x,pd Omega):=inf_{yinpd Omega}|x-y|$. The integral term $int_Omega dist^p(x,pd Omega )d x$ quantifies the easiness for points in $Omega$ to reach the boundary, while $frac{H^1(pd Omega)}{H^2(Omega)}$ is the perimeter-to-area ratio. The main aim is to prove existence and $C^{1,1}$-regularity of minimizers of $E$." @default.
- W4285703977 created "2022-07-18" @default.
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- W4285703977 date "2022-01-25" @default.
- W4285703977 modified "2023-09-27" @default.
- W4285703977 title "The average distance problem with perimeter-to-area ratio penalization" @default.
- W4285703977 doi "https://doi.org/10.48550/arxiv.2201.10100" @default.
- W4285703977 hasPublicationYear "2022" @default.
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