Boundary Value Problems for Elliptic Systems

Zusammenfassung This book examines the theory of boundary value problems for elliptic systems of partial differential equations. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. Inhaltsverzeichnis 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.

Product details

• Authors: B. Lawruk, Lawruk B., B. Rowley, Rowley B., J. T. Wloka, J. T. (Christian-Albrechts Universitat Zu K Wloka, J. T. Rowley Wloka, J.t. Rowley Wloka, Joseph Wloka, Wloka J. T.
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 28.07.1995
• EAN: 9780521430111
• ISBN: 978-0-521-43011-1
• No. of pages: 656
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / General, Differential calculus & equations, Differential calculus and equations