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Linear elliptic boundary value problems in varying domains

✍ Scribed by Marius Bochniak

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
132 KB
Volume
250
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The paper is devoted to the study of solutions to linear elliptic boundary value problems in domains depending smoothly on a small perturbation parameter. To this end we transform the boundary value problem onto a fixed reference domain and obtain a problem in a fixed domain but with differential operators depending on the perturbation parameter. Using the Fredholm property of the underlying operator we show the differentiability of the transformed solution under the assumption that the dimension of the kernel does not depend on the perturbation parameter. Furthermore, we obtain an explicit representation for the corresponding derivative.

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