McLean W. Strongly Elliptic Systems and Boundary Integral Equations

Cambridge: Cambridge University Press, 2000. — 357 p.Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity.
The book is designed to provide an ideal preparation for studying the modern research literature on boundary element methods.