The aim of this monograph is to provide a theoretical background and introduce certain computational methods for the investigation of boundary singularities in elliptic problems. The authors’ main concerns are elasticity problems featuring sharp corners, composite materials, or cracks. Obviously, such situations are of great importance in a wide range of physical processes.

The book is set out as a series of ten lectures, which are not of equal length; lectures 1 to 4 cover much of the background theory. The first, and introductory, lecture nicely outlines the relevance of singular elliptic problems but concludes with an explanation of the notation to be used throughout the remainder of the text, which is usually a bad omen. Indeed, my fears were soon realized. The monograph is aimed, according to the cover, at research workers in the applied and engineering sciences, but the presentation assumes a knowledge of mathematical terminology and ideas I doubt many engineers and applied scientists possess. I suspect the monograph will be of interest to some mathematicians but few practitioners.

The latter half of the book concentrates on particular types of problems and methods for determining the form of the singularities that arise. The computational methods presented are for finding the form of the singular behavior and are not concerned with techniques for estimating a global numerical solution to a particular physical situation. In this respect, I was misled by the title and consequently was rather disappointed by the book. To discover the nature of a singular point in an elliptic problem is merely one aspect of the problem. A major issue is how best to exploit the information to produce an accurate numerical solution. Also, such considerations have to be tempered with the engineer’s view that the singularity is merely an idealization of a more complex process.