Titlebook: Singular Integral Equations; Boundary problems of N. I. Muskhelishvili Book 1958 Wolters-Noordhoff Publishing 1958 Integral equation

无关紧要

Cauchy Integrals near ends of the Line of Integrationmental in the later work, whenever boundary problems or singular integral equations are considered for which the boundary or line of integration contains arcs. The results obtained below also find application in the more general case in which the density has discontinuities at several points on the

OTTER

The Hilbert and Riemann-Hilbert Boundary Problemsig. 8, § 24). The contour . may be absent in which case . is an infinite region (the plane with holes). By . will be denoted the union of .,. … .(as before the positive direction of . will be such that . lies to the left when . is described in that direction), by . that part of the plane which is th

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The Dirichlet Problemderstood the union of these contours; as usual, the positive direction on . will be taken such that . remains on the left. The contour L. may be absent in which case . is infinite. The union of the finite regions S., …, . contained in . …, . respectively, and (in the presence of .) the infinite regi

interior

Various Representations of Holomorphic Functions by Cauchy and Analogous Integralsc function in the form of a Cauchy or analogous integral; this expression, substituted into the boundary condition, reduces to an integral equation. In fact, such a method was used in the last section for the solution of the classical and modified Dirichlet problems.

南极

Infantry

Effective Solution of the Principal Problems of the Static Theory of Elasticity for the Half- Plane,ne with straight cuts. The method stated was given by the Author in the papers [9], [10], [11] and applied to the half-plane and plane with straight cuts. This method was applied to the case of the circle by the post-graduate student I. N. Kartsivadze [1].

Ascendancy

Singular Integral Equations for the Case of Arcs and Continuous Coefficients A. Kveselava [1]. In this latter paper the concept of classes of solutions was introduced for the first time and the fundamental theorems of § 112 were proved. In addition, another method of investigation due to D. A. Kveselava [1] is given in § 115.

夹克怕包裹

Singular Integral Equations in the case of Discontinuous Coefficientsxed points on ., taken ia the same order in which they are encountered on traversing . in the positive direction, and . .,…, . will be the same points, taken in any order. The classes of functions ., given on ., will refer to these points.