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Technical Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations
Posted on 2010-04-15
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More Dan Henry, Jack Hale, Antônio Luiz Pereira, " Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations (London Mathematical Society Lecture Note Series)" 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 authors 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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