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Picard, Rainer / McGhee, Des

Partial Differential Equations

A unified Hilbert Space Approach

Series:De Gruyter Expositions in Mathematics 55

    159,95 € / $224.00 / £145.50*

    eBook (PDF)
    Publication Date:
    June 2011
    Copyright year:
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    • Global access to PDEs
    • With detailed proofs
    • For studends, researchers and also for self-study

    Aims and Scope

    This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces.

    The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations.

    In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented.

    The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics.

    Supplementary Information


    xviii, 469 pages
    Type of Publication:
    Mathematics; Partial Differential Equations; Hilbert Space; Sobolev; Evolution Equation

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    Rainer Picard, Dresden University of Technology, Germany; Des McGhee, University of Strathclyde, Glasgow, Scotland, UK.

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