The Hilbert and Riemann-Hilbert Boundary Problems

N. I. Muskhelishvili
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N. I. Muskhelishvili: Institute of Mathematics Tiflis

Chapter Chapter 5 in Singular Integral Equations, 1958, pp 86-112 from Springer

Abstract: Abstract Let S + be a connected region, bounded by smooth contours Lo, L1 x2026; Lp, not intersecting one another, the first of which encloses all the others (cf. Fig. 8, § 24). The contour L o may be absent in which case S + is an infinite region (the plane with holes). By L will be denoted the union of Lo,L1 … Lp(as before the positive direction of L will be such that S+ lies to the left when L is described in that direction), by S− that part of the plane which is the complement of S+ + L, by So−, S1−… Sp− the components of S−, bounded respectively by Lo, L1 … Lp (the first of those regions is absent, if there is no Lo; So− is infinite, if Lo exists).

Keywords: General Solution; Holomorphic Function; Dirichlet Problem; Fundamental Solution; Conformal Transformation (search for similar items in EconPapers)
Date: 1958
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DOI: 10.1007/978-94-009-9994-7_5

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