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The Hilbert Problem in the Case of Arcs or Discontinuous Boundary Conditions

In: Singular Integral Equations

Author

Listed:
  • N. I. Muskhelishvili

    (Institute of Mathematics Tiflis)

Abstract

1°. Up to and including § 85, L will be understood to be the union of smooth, non-intersecting arcs L1 L2, …, Lp with definite positive directions. The ends of the arcs L1 (j = 1,2,…, p) will be denoted by aj, bj in such a way that the positive direction of Lj is from aj, to bj; “the ends a” and “the ends b” will sometimes be distinguished accordingly. When it is of no importance which end is referred to, it will be denoted by c or cj. The plane cut along L = L1 + L2 + … + Lj will be denoted by S; the boundary L does not belong to S.

Suggested Citation

  • N. I. Muskhelishvili, 1958. "The Hilbert Problem in the Case of Arcs or Discontinuous Boundary Conditions," Springer Books, in: Singular Integral Equations, chapter 0, pages 227-248, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-9994-7_10
    DOI: 10.1007/978-94-009-9994-7_10
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