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  3. Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations
  • Cited by 82
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2005
Online ISBN:
9780511546730
DOI:
https://doi.org/10.1017/CBO9780511546730
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
Series:
London Mathematical Society Lecture Note Series (318)
Information

Book description

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. In this book, first published in 2005, 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.

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