Boundary integral equations

George C. Hsiao, Wolfgang L. Wendland9783540152842, 9783540685456, 3540152849

This book is devoted to the basic mathematical properties of solutions to boundary integral equations and presents a systematic approach to the variational methods for the boundary integral equations arising in elasticity, fluid mechanics, and acoustic scattering theory. It may also serve as the mathematical foundation of the boundary element methods. The latter have recently become extremely popular and efficient computational tools in applications. The authors are well known for their fundamental work on boundary integral equations and related topics. This book is a major scholarly contribution to the modern theory of boundary integral equations and should be accessible and useful to a large community of mathematical analysts, applied mathematicians, engineers and scientists.

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Table of contents :
Cover……Page 1
Applied Mathematical Sciences Volume 164……Page 2
Series Title……Page 3
Title……Page 4
Copyright……Page 5
Dedication……Page 6
Preface……Page 7
Table of Contents……Page 13
1. Introduction……Page 18
2. Boundary Integral Equations……Page 41
3. Representation Formulae, Local Coordinates and Direct Boundary Integral Equations……Page 111
4. Sobolev Spaces……Page 175
5. Variational Formulations……Page 211
6. Introduction to Pseudodifferential Operators……Page 319
7. Pseudodifferential Operators as Integral Operators……Page 369
8. Pseudodifferential and Boundary Integral Operators……Page 429
9. Integral Equations on Γ⊂ IR3 Recast as Pseudodifferential Equations……Page 509
10. Boundary Integral Equations on Curves in IR2……Page 564
A. Differential Operators in Local Coordinates with Minimal Differentiability……Page 608
References……Page 614
Index……Page 628
Applied Mathematical Sciences……Page 634