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    Function Spaces and Partial Differential Equations: Volume 2 - Contemporary Analysis

    Function Spaces and Partial Differential Equations by Taheri, Ali;

    Volume 2 - Contemporary Analysis

    Series: Oxford Lecture Series in Mathematics and Its Applications;

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    Product details:

    • Publisher OUP Oxford
    • Date of Publication 30 July 2015

    • ISBN 9780198733157
    • Binding Hardback
    • No. of pages480 pages
    • Size 235x162x28 mm
    • Weight 890 g
    • Language English
    • Illustrations 8
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    Short description:

    This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.

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    Long description:

    This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

    The book is clearly written and is a valuable addition to the literature. It is warmly recommended to the graduate student. For the instructor, it is an excellent resource for graduate courses and seminars in analysis and partial differential equations.

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    Table of Contents:

    Maximal Function; Bounding Averages and Pointwise Convergence
    Harmonic-Hardy Spaces hp(H)
    Sobolev Spaces; A Resolution of the Dirichlet Principle
    Singular Integral Operators and Vector-Valued Inequalities
    Littlewood-Paley Theory, Lp-Multipliers and Function Spaces
    Morrey and Campanato vs. Hardy and John-Nirenberg Spaces
    Layered Potentials, Jump Relations and Existence Theorems
    Second Order Equations in Divergence Form: Continuous Coefficients
    Second Order Equations in Divergence Form: Measurable Coefficients
    Partition of Unity
    Total Boundedness and Compact Subsets of Lp
    Gamma and Beta Functions
    Volume of the Unit n-Ball
    Integrals Related to Abel and Gauss Kernels
    Hausdorff Measures Hs
    Evaluation of Some Integrals Over
    Sobolev Spaces

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