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Boundary Value Problems for Elliptic Systems


  • Authors:
  • J. T. Wloka, Christian-Albrechts Universität zu Kiel, Germany
  • B. Rowley, Champlain College, Lennoxville
  • B. Lawruk, McGill University, Montréal
  • Date Published: April 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521061438

£ 45.99

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About the Authors
  • This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

    • Includes more than one hundred and fifty exercises
    • Introduces many new methods and results
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    Reviews & endorsements

    'It is the strength of this book that, for the first time, the theory of (elliptic) systems is presented on the level of recent research theory of (scalar) pseudodifferential operators … the authors put new life into the classical method of shifting boundary value problems in a domain to its boundary.' Hans Triebel, Bulletin of the London Mathematical Society

    'The book can be recommended both as a textbook for graduate students and as a handbook for researchers.' T. Weidl, Proceedings of the Edinburgh Mathematical Society

    '… certainly of great interest for specialists and can be used for advanced lectures or seminars in this field.' Monatshefte für Mathematik

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    Product details

    • Date Published: April 2008
    • format: Paperback
    • isbn: 9780521061438
    • length: 656 pages
    • dimensions: 245 x 175 x 35 mm
    • weight: 0.91kg
    • contains: 8 b/w illus. 173 exercises
    • availability: Available
  • Table of Contents

    Part I. A Spectral Theory of Matrix Polynormials:
    1. Matrix polynomials
    2. Spectral triples for matrix polynomials
    3. Monic matrix polynomials
    4. Further results
    Part II. Manifolds and Vector Bundles:
    5. Manifolds and vector bundles
    6. Differential forms
    Part III. Pseudo-Differential Operators and Elliptic Boundary Value Problems:
    7. Pseudo-differential operators on Rn
    8. Pseudo-differential operators on a compact manifold
    9. Elliptic systems on bounded domains in Rn
    Part IV. Reduction Of A Boundary Value Problem To An Elliptic System On The Boundary:
    10. Understanding the L-condition
    11. Applications to the index
    12. BVPs for ordinary differential operators and the connection with spectral triples
    13. Behaviour of a pseudo-differential operator near a boundary
    14. The Main Theorem revisited
    Part V. An Index Formula For Elliptic Boundary Problems In The Plane:
    15. Further results on the Lopatinskii Condition
    16. The index in the plane
    17. Elliptic systems with 2 x 2 real coefficients.

  • Authors

    J. T. Wloka, Christian-Albrechts Universität zu Kiel, Germany

    B. Rowley, Champlain College, Lennoxville

    B. Lawruk, McGill University, Montréal

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