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A multielement boundary-value problem with a piecewise-smooth shift on a piecewise-Lyapunov contour for a function analytic in a domain

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Ukrainian Mathematical Journal Aims and scope

Abstract

In an Lp-formulation (1 < p < ∞) there is constructed for a function ϕ (z) analytic in a multiconnected domain with a piecewise-Lyapunov boundary Γ a Noether theory of the boundary-value problem

$$a (t) \varphi (t) + b (t) \varphi [\alpha (t)] + d (t\overline {) \varphi (t) } + e (t) \overline {\varphi [\alpha (t)]} = f(t), t \varepsilon \Gamma ,$$

wherea, b, d, and e are piecewise-continuous functions on Γ,a: Γ → Γ is an orientation-preserving piecewise-smooth Carleman shift and, moreover, certain constraints are imposed on the free term f and the coefficientsa, b, d, and e.

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Literature cited

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Authors and Affiliations

  1. Odessa University, USSR

    Z. M. Lysenko & A. P. Nechaev

Authors
  1. Z. M. Lysenko
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  2. A. P. Nechaev
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1063–1068, August, 1990.

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Lysenko, Z.M., Nechaev, A.P. A multielement boundary-value problem with a piecewise-smooth shift on a piecewise-Lyapunov contour for a function analytic in a domain. Ukr Math J 42, 948–952 (1990). https://doi.org/10.1007/BF01099226

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  • DOI: https://doi.org/10.1007/BF01099226

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