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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