The Dirichlet Problem

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

Chapter Chapter 7 in Singular Integral Equations, 1958, pp 163-186 from Springer

Abstract: Abstract Let S + be a connected region, bounded by simple smooth non- intersecting contours Lo, L1 …, LP the first of which contains all the others. By L will be understood the union of these contours; as usual, the positive direction on L will be taken such that S + remains on the left. The contour Lo may be absent in which case S+ is infinite. The union of the finite regions S1−, …, Sp− contained in L1 …, Lp respectively, and (in the presence of Lo) the infinite region So consisting of the points outside Lo, will be denoted by S.

Keywords: Harmonic Function; Dirichlet Problem; Boundary Problem; Homogeneous Equation; Singular Integral Equation (search for similar items in EconPapers)
Date: 1958
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DOI: 10.1007/978-94-009-9994-7_7

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