§15§The book is devoted to the methods and results of the integral equations theory for elasticity problems. It consists of two parts and appendix. The first part contains a survey of mathematical topics necessary for understanding the main aspects of this course.The mathematical background is presented within the first part in detail. The second part deals with the most important results in the theory of boundary integral equations. It also discusses some new aspects of this theory which have been suggested by the authors, including the following problems: the theory of elasticity for an anisotropic medium, new type of integral equations (Pobedria's type), contact problems, fracture mechanics and Cosserat spectrum. The applications in fracture mechanics go well beyond merely illustrating the methods: they yield new results in some classical problems. This book is of interest to applied mechanicians, engineers, mathematicians and students interested in boundary ele §15§ment method and its applications. §03§Integral Equations.- General Results on Linear Integral Equations.- One-Dimensional Singular Integral Equations.- Two-Dimensional Singular Integral Equations.- Approximate Solution of Integral Equations.- Problems of the Theory of Elasticity and Cracks Mechanics.- The Integral Equations of Classical Two-Dimensional Problems.- Potential Theory for Basic Three-Dimensional Problems.- The Contact Problems of the Theory of Elasticity.- Problems of the Theory of Cracks.
