TY  - BOOK
AU  - Henry,Dan
TI  - Perturbation of the boundary in boundary-value problems of partial differential equations
T2  - London Mathematical Society lecture note series
SN  - 9780511546730 (ebook)
AV  - QA379 .H46 2005
U1  - 515/.353 22
PY  - 2005///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Boundary value problems
KW  - Perturbation (Mathematics)
KW  - Differential equations, Partial
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Geometrical preliminaries -- Differential calculus of boundary perturbations -- Examples using the implicit function theorem -- Bifurcation problems -- The tranversality theorem -- Generic perturbation of the boundary -- Boundary operators for second-order elliptic equations -- The method of rapidly-oscillating solutions
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511546730
ER  -