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muskhelishvili singular integral equations djvu
where is a polynomial of degree n with coefficients depending on the parameter α. Then the Cauchy integrals on the both parts of (12) are evaluated analytically by using equations given in Sect. 110 of [18]; analogous formulae for the Hadamard integrals are promptly obtained by integration by parts.
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problems, the Dirichlet problem, inversion formulas for arcs, and many other areas. Intended for graduate students, applied and pure mathematicians, engineers, physicists, and researchers in a variety of scientific and industrial fields, this text is accessible to students acquainted with the basic theory of functions of a complex variable and the theory of Fredholm integral equations.
Boundary integral equations of elasticity theory in a plane domain with a peak at the boundary are considered. Solvability and uniqueness theorems as well as results on the asymptotic behaviour of solutions near the peak are obtained.
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