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Monotone variations of the first eigenvalue for doubly connected domains

✍ Scribed by Chie–Ping Chu; Chih Chy Fwu

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 203 KB
Volume: 256
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310066

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The first Dirichlet eigenvalue for the Laplace operator of a doubly connected plane domain varies with the relative position of the inner hole. Under certain mild hypothesis it decreases as the two boundary curves get closer along some specific direction. We made this observation by analyzing level curves and rearrangement technique.

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