Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations

Dan Henry - Collection London Mathematical Society Student Texts

206 pages, parution le 19/05/2005

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Résumé

Perturbation of the boundary is a rather neglected topic in the study of PDEs for two main reasons. First, on the surface it appears trivial, merely a change of variables and an application of the chain rule.
Second, carrying out such a change of variables frequently results in long and difficult calculations. Here the author carefully discusses a calculus that allows the computational morass to be bypassed, and he goes on to develop more general forms of standard theorems, which help answer a wide range of problems involving boundary perturbations. Many examples are presented to demonstrate the usefulness of the author's approach, while on the other hand many tantalizing open questions remain. Anyone whose research involves PDEs will find something of interest in this book.

Unique treatment of this subject
Clearly written
Author was world authority on this material

Sommaire

Introduction
Geometrical preliminaries
Differential calculus of boundary perturbations
Examples using the implicit function theorem
Bifurcation problems
The transversality theorem
Generic perturbation of the boundary
Boundary operators for second-order elliptic equations
The method of rapidly-oscillating solutions.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Dan Henry
Collection	London Mathematical Society Student Texts
Parution	19/05/2005
Nb. de pages	206
Format	15 x 22,5
Couverture	Broché
Poids	300g
Intérieur	Noir et Blanc
EAN13	9780521574914
ISBN13	978-0-521-57491-4