𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Level sets of the first eigenfunction from the rearrangement point of view

✍ Scribed by Chie-Ping Chu

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
281 KB
Volume
277
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

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)

πŸ“œ SIMILAR VOLUMES

Convexity in x of the level sets of the
Convexity in x of the level sets of the first Dirichlet eigenfunction
✍ Chie-Ping Chu πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 168 KB

## 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)

From the patient's point of view
From the patient's point of view
✍ Kenneth H. Crandall πŸ“‚ Article πŸ“… 1966 πŸ› Springer 🌐 English βš– 146 KB
Color from the physical point of view
Color from the physical point of view
πŸ“‚ Article πŸ“… 1918 πŸ› Elsevier Science 🌐 English βš– 148 KB

It contains a list of the gauging stations maintained on the islands, estimates of the daily and monthly discharge of the streams, and the results of studies of rainfall at many points. Water-Supply Paper 318 gives the results of water-resource investigations in Hawaii for the years I9O9-I9ti, Water