Boundary Integral Equations

George C. Hsiao, Wolfgang L. Wendland (auth.)3540152849, 978-3-540-15284-2, 978-3-540-68545-6

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.

Table of contents :
Front Matter….Pages i-xix
Introduction….Pages 1-23
Boundary Integral Equations….Pages 25-94
Representation Formulae, Local Coordinates and Direct Boundary Integral Equations….Pages 95-158
Sobolev Spaces….Pages 159-194
Variational Formulations….Pages 195-302
Introduction to Pseudodifferential Operators….Pages 303-352
Pseudodifferential Operators as Integral Operators….Pages 353-412
Pseudodifferential and Boundary Integral Operators….Pages 413-492
Integral Equations on Γ⊂ IR 3 Recast as Pseudodifferential Equations….Pages 493-547
Boundary Integral Equations on Curves in IR 2 ….Pages 549-598
Back Matter….Pages 599-618