Boundary Value Problems for Elliptic Systems

This book examines the theory of boundary value problems for elliptic systems of partial differential equations.

J. T. Wloka (Author), B. Rowley (Author), B. Lawruk (Author)

9780521430111, Cambridge University Press

Hardback, published 28 July 1995

656 pages, 8 b/w illus. 173 exercises
24.2 x 16.3 x 4 cm, 1.03 kg

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

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.

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.

Subject Areas: Differential calculus & equations [PBKJ]