Singular Integral Equations: Boundary problems of functions theory and their applications to mathematical physics

✍ Scribed by N. I. Muskhelishvili (auth.)

• Publisher: Springer Netherlands
• Year: 1977
• Tongue: English
• Leaves: 452
• Edition: 1
• Category: Library

✦ Synopsis

In preparing this translation for publication certain minor modifications and additions have been introduced into the original Russian text, in order to increase its readibility and usefulness. Thus, instead of the first person, the third person has been used throughout; wherever possible footnotes have been included with the main text. The chapters and their subsections of the Russian edition have been renamed parts and chapters respectively and the last have been numbered consecutively. An authors and subject index has been added. In particular, the former has been combined with the list of references of the original text, in order to enable the reader to find quickly all information on anyone reference in which he may be especially interested. This has been considered most important with a view to the difficulties experienced outside Russia in obtaining references, published in that country. Russian names have been printed in Russian letters in the authors index, in order to overcome any possible confusion arising from transliteration.

✦ Table of Contents

Front Matter....Pages i-xiv
The Hölder Condition....Pages 7-21
Integrals of the Cauchy Type....Pages 22-55
Some Corollaries on Cauchy Integrals....Pages 56-72
Cauchy Integrals near ends of the Line of Integration....Pages 73-85
The Hilbert and Riemann-Hilbert Boundary Problems....Pages 86-112
Singular Integral Equations with Cauchy Type Kernels (Case of Contours)....Pages 113-162
The Dirichlet Problem....Pages 163-186
Various Representations of Holomorphic Functions by Cauchy and Analogous Integrals....Pages 187-201
Solution of the Generalized Riemann-Hilbert- Poincaré Problem....Pages 202-226
The Hilbert Problem in the Case of Arcs or Discontinuous Boundary Conditions....Pages 227-248
Inversion Formulae for Arcs....Pages 249-260
Effective Solution of Some Boundary Problems of the Theory of Harmonic Functions....Pages 261-281
Effective Solution of the Principal Problems of the Static Theory of Elasticity for the Half- Plane, Circle and Analogous Regions....Pages 282-322
Singular Integral Equations for the Case of Arcs and Continuous Coefficients....Pages 323-355
Singular Integral Equations in the case of Discontinuous Coefficients....Pages 356-358
Application to the Dirichlet and Similar Problems....Pages 359-372
Solution of the Integro-Differential Equation of the theory of Aircraft Wings of Finite Span....Pages 373-379
Front Matter....Pages 380-380
The Hilbert Problem for Several Unknown Functions....Pages 381-414
Systems of Singular Integral Equations with Cauchy type Kernels and Some Supplements....Pages 415-423
Back Matter....Pages 424-447

✦ Subjects

Integral Equations;Mechanics