Boundary Value Problems for Elliptic Systems

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Paperback | 24 April 2008

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656 Pages

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23.39 x 15.6 x 3.35

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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.

Industry Reviews

'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 fur Mathematik

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A Spectral Theory of Matrix Polynormials
Matrix polynomials
Spectral triples for matrix polynomials
Monic matrix polynomials
Further results
Manifolds and Vector Bundles
Manifolds and vector bundles
Differential forms
Pseudo-Differential Operators and Elliptic Boundary Value Problems
Pseudo-differential operators on Rn
Pseudo-differential operators on a compact manifold
Elliptic systems on bounded domains in Rn
Reduction Of A Boundary Value Problem To An Elliptic System On The Boundary
Understanding the L-condition
Applications to the index
BVPs for ordinary differential operators and the connection with spectral triples
Behaviour of a pseudo-differential operator near a boundary
The Main Theorem revisited
An Index Formula For Elliptic Boundary Problems In The Plane
Further results on the Lopatinskii Condition
The index in the plane
Elliptic systems with 2 x 2 real coefficients
Table of Contents provided by Publisher. All Rights Reserved.

Boundary Value Problems for Elliptic Systems

At a Glance

Paperback

Industry Reviews

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How to return your order

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