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

This monograph gives a description of all algorithmic steps and a mathematical foundation for a special numerical method, namely the boundary-domain integral method (BDIM). This method is a generalization of the well-known boundary element method, but it is also applicable to linear elliptic systems with variable coefficients, especially to shell equations. The text should be understandable at the beginning graduate-level. It is addressed to researchers in the fields of numerical analysis and computational mechanics, and will be of interest to everyone looking at serious alternatives to the well-established finite element methods.

A systematic examination of classical and non-classical problems for linear partial differential equations and systems of elliptic, hyperbolic and mixed types. Among a number of difficult problems addressed are the Dirichlet and oblique derivative problems for non- uniformly elliptic equations and non-strongly elliptic systems and the Cauchy and Darloux problems for non-strongly hyperbolic systems and hyperbolic equations with parabolic degeneracy on the boundary. Written at a level suitable for undergraduate and graduate students and researchers. Individual price, $89. Annotation copyrighted by Book News, Inc., Portland, OR

The proceedings covers the following topics: Boundary value problems of partial differential equations including free boundary problems; Theory and methods of integral equations including singular integral equations; Applications of integral equations and boundary value problems to mechanics and physics; and numerical methods for integral equations and boundary value problems.