Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Windows of given area
with minimal heat diffusion

Author: Jochen Denzler
Journal: Trans. Amer. Math. Soc. 351 (1999), 569-580
MSC (1991): Primary 49J40; Secondary 49J10, 35J20, 35R05
MathSciNet review: 1475680
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Abstract: For a bounded Lipschitz domain $\Omega$, we show the existence of a measurable set $D\subset \partial\Omega$ of given area such that the first eigenvalue of the Laplacian with Dirichlet conditions on $D$ and Neumann conditions on $\partial \Omega \setminus D$ becomes minimal. If $\Omega$ is a ball, $D$ will be a spherical cap.

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Jochen Denzler
Affiliation: Mathematisches Institut, Ludwig–Maximilians–Universität, Theresienstraße 39, D–80333 München, Germany
Address at time of publication: Zentrum Mathematik, Technische Universität, Arcisstrasse 21, D-80290 München, Germany

Received by editor(s): November 16, 1996
Article copyright: © Copyright 1999 American Mathematical Society