STRONGLY ELLIPTIC SYSTEMS AND BOUNDARY INTEGRAL EQUATIONS

Le Monde En Tique

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Ouvrage 9780521663755 : STRONGLY ELLIPTIC SYSTEMS AND BOUNDARY INTEGRAL EQUATIONS

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book is designed to provide an ideal preparation for studying the modern research literature on boundary element methods.
• Emphasises Fredholm integrals of the first kind, now preferred for numerical methods
• Provides a solid background in Sobolev spaces
Contents
Introduction; 1. Abstract linear equations; 2. Sobolev spaces; 3. Strongly elliptic systems; 4. Homogeneous distributions; 5. Surface potentials; 6. Boundary integral equations; 7. The Laplace equation; 8. The Helmholtz equation; 9. Linear elasticity; Appendix A. Extension operators for Sobolev spaces; Appendix B. Interpolation spaces; Appendix C. Further properties of spherical harmonics; Index of notation; Index.


Auteur : MCLEAN
Editeur : CAMBRIDGE UNIVERSITY PRESS
Nombre de pages : 376
Date de publication : 03 2000

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