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Elliptic Differential Operators and Spectral Analysis

  • D. E. Edmunds
  • W.D. Evans

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. David E. Edmunds, W. Desmond Evans
    Pages 1-33
  3. David E. Edmunds, W. Desmond Evans
    Pages 35-56
  4. David E. Edmunds, W. Desmond Evans
    Pages 57-63
  5. David E. Edmunds, W. Desmond Evans
    Pages 65-81
  6. David E. Edmunds, W. Desmond Evans
    Pages 83-113
  7. David E. Edmunds, W. Desmond Evans
    Pages 115-158
  8. David E. Edmunds, W. Desmond Evans
    Pages 159-202
  9. David E. Edmunds, W. Desmond Evans
    Pages 203-211
  10. David E. Edmunds, W. Desmond Evans
    Pages 213-233
  11. David E. Edmunds, W. Desmond Evans
    Pages 235-247
  12. David E. Edmunds, W. Desmond Evans
    Pages 249-280
  13. David E. Edmunds, W. Desmond Evans
    Pages 281-301
  14. Back Matter
    Pages 303-322

About this book

Introduction

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature.

Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included.

Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.

Keywords

Elliptic operators self-adjoint extensions Sobolev spaces p-Laplacian spectral theory Schauder estimates regularity theory Dirac operator

Authors and affiliations

  • D. E. Edmunds
    • 1
  • W.D. Evans
    • 2
  1. 1.Department of MathematicsUniversity of SussexBrightonUK
  2. 2.School of MathematicsUniversity of CardiffCardiffUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02125-2
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02124-5
  • Online ISBN 978-3-030-02125-2
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site