Strongly Elliptic Systems and Boundary Integral Equations

This 2000 book provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains.

William McLean (Author)

9780521663328, Cambridge University Press

Hardback, published 13 February 2000

372 pages, 4 b/w illus.
23.7 x 16 x 2.6 cm, 0.64 kg

'The author is to be congratulated on successfully establishing a bridge between basic undergraduate material and the modern research literature in boundary element methods … Compliments are due both to the author and also to his numerous associates - duly acknowledged in the preface - for generating a concise and professional presentation of conceptually difficult material.' The Mathematical Gazette

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book, first published in 2000, treats one class of such equations, concentrating on methods involving the use of surface potentials. It provided 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.

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.

Subject Areas: Numerical analysis [PBKS]