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Jochen Denzler: Windows of given area with minimal heat diffusion
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Transactions of the AMS 351 (1999), 569-580

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For a bounded Lipschitz domain~$\Omega$, we show the existence of a measurable 
set~$D\subset\boundary\Omega$ of given area such that the first eigenvalue
of the Laplacian with Dirichlet conditions on~$D$ and Neumann conditions
on~$\boundary\Omega\setminus D$ becomes minimal. If $\Omega$~is a ball,
$D$~will be a spherical cap. 
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