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Convexity in x of the level sets of the first Dirichlet eigenfunction

✍ Scribed by Chie-Ping Chu

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
168 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

On a planar domain which is convex in x, the level sets of the first Dirichlet eigenfunction for Laplacian are also convex in x. This gives an affirmative answer to a conjecture proposed by B. Kawohl. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Level sets of the first eigenfunction fr
Level sets of the first eigenfunction from the rearrangement point of view
✍ Chie-Ping Chu πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 281 KB

## Abstract The level curves of the first Dirichlet eigenfunction for the Laplace operator of a convex plane domain is convex. We make this observation by a new rearrangement technique. (Β© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)