Strongly Elliptic Systems and Boundary Integral Equations
Strongly Elliptic Systems and Boundary Integral Equations
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USDPartial 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. William McLean 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 affords an ideal background 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
- Ideal as a textbook for graduate courses
Reviews & endorsements
"Overall, this is a very readable account, well-suited for people interested in boundary integral and element methods. It should be particularly useful to the numerical analysts who seek a broader and deeper understanding of the non-numerical theory." Mathematical Reviews
Product details
January 2000Paperback
9780521663755
372 pages
229 × 152 × 23 mm
0.512kg
4 b/w illus.
Available
Table of 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.
