It was the last book the outstanding mathematician, mechanician and
lecturer S. G. Mikhlin took an active part in writing. Having been
completed during his lifetime, this book could not be published in
Russia due to well- know difficulties. Since that time new results in
integral equations of elasticity theory have appeared. The works of W.
Wendland and his school on numerical methods of solving boundary
integral equations, the works of I. Chudinovich on inves- tigation of
non-stationary integral equations, the works of S. Kuznetsov con- nected
with the construction of the fundamental solutions for anisotropic me-
dia and others deserve special mentioning. The authors recognize that
though the book is devoted to integral equations of elasticity theory,
its contents do not cover all possible directions in this field. So the
book does not contain the investigations of pseudo-differential
equations of three-dimensional prob- lems of elasticity theory,
connected with the works of R. Goldstein, I. Klein, G. Eskin; the
questions of solving by integral transformations (I. Ufland, L. Slepian,
B. Buda. e: v); the theory of symbols of pseudo-differential operators
on non-smooth surfaces developed in the works of B. Plamenevski et al.
and the new methods of numerical solution of pseudo-differential
equations as developed by a school of V. Mazya. The present book gives
the classical methods of potential theory in elas- ticity and their
development and also the solution of a number of problems which here are
published in English for the first time.
