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- W2952058189 abstract "We consider the problem of maximizing the first eigenvalue of the $p$-laplacian (possibly with non-constant coefficients) over a fixed domain $Omega$, with Dirichlet conditions along $partialOmega$ and along a supplementary set $Sigma$, which is the unknown of the optimization problem. The set $Sigma$, that plays the role of a supplementary stiffening rib for a membrane $Omega$, is a compact connected set (e.g. a curve or a connected system of curves) that can be placed anywhere in $overline{Omega}$, and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $Sigma$ from spreading throughout $Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $Sigma_L$ as $Ltoinfty$ via $Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $ptoinfty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $infty$-laplacian." @default.
- W2952058189 created "2019-06-27" @default.
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- W2952058189 date "2018-03-29" @default.
- W2952058189 modified "2023-10-01" @default.
- W2952058189 title "Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length" @default.
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