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Jump boundary-value problem on a contour with elongate singularities

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Abstract

Let Γ be image of interval (0, 1) under one-to-one continuous mapping φ: (0, 1) → C. If closure of Γ differs from the set Γ bymore than two points, then we call Γ the contour with elongate singularities.

We study boundary-value jump problems for analytical functions on that contours, and obtain new criteria for their solvability.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    B. A. Kats

  2. Kazan National Research Technical University named after A. N. Tupolev, ul. K. Marksa 10, Kazan, 420111, Russia

    S. R. Mironova

  3. Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

    A. Yu. Pogodina

Authors
  1. B. A. Kats
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  2. S. R. Mironova
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  3. A. Yu. Pogodina
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Corresponding author

Correspondence to B. A. Kats.

Additional information

Original Russian Text © B.A. Kats, S.R. Mironova, A.Yu. Pogodina, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 1, pp. 12–16.

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Kats, B.A., Mironova, S.R. & Pogodina, A.Y. Jump boundary-value problem on a contour with elongate singularities. Russ Math. 61, 10–13 (2017). https://doi.org/10.3103/S1066369X17010029

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  • DOI: https://doi.org/10.3103/S1066369X17010029

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