Windows of given area with minimal heat diffusion
Jochen Denzler · Transactions of the American Mathematical Society · 1999
For a bounded Lipschitz domain Ω \Omega , we show the existence of a measurable set D ⊂ ∂ Ω D\subset \partial \Omega of given area such that the first eigenvalue of the Laplacian with Dirichlet conditions on D D and Neumann conditions on ∂ Ω ∖ D \partial \Omega \setminus D becomes minimal. If Ω \Omega is a ball, D D will be a spherical cap.