Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 151–160 | Cite as

Classes of Finite Solutions to the Inverse Problem of the Logarithmic Potential

  • N. R. Abubakirov
  • L. A. Aksentev


We obtain a new class of solutions to the inverse problems of the logarithmic potential in the form of a logarithmic function of a ratio of polynomials of the same degree. We give examples of finite solvability of the inverse problems.

Keywords and phrases

logarithmic potential integral equation univalence starlike 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. M. Rapoport, “The planar inverse problem of potential theory,” Dokl. Akad. Nauk SSSR 28, 305–307 (1940).zbMATHGoogle Scholar
  2. 2.
    I. M. Rapoport, “One problem of the potential theory,” Ukr. Math. J. 2 (2), 48–55 (1950).zbMATHGoogle Scholar
  3. 3.
    V. K. Ivanov, “Integral equation for the inverse logarithmic equation problem,” Dokl. Akad. Nauk SSSR 105, 409–412 (1955).MathSciNetGoogle Scholar
  4. 4.
    V. K. Ivanov, “On the solubility of the inverse problem of the logarithmic potential in finite form,” Dokl. Akad. Nauk SSSR 106, 598–599 (1956).MathSciNetGoogle Scholar
  5. 5.
    G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Vol. 26 of Transl. Math. Mongraphs (Am.Math. Soc., Providence, 1969).CrossRefzbMATHGoogle Scholar
  6. 6.
    P. S. Novikov, “On uniqueness of the inverse problem of the theory of potential,” Dokl. Acad. Sci. USSR 18, 165–168 (1938).Google Scholar
  7. 7.
    M. A. Lavrentev and B. V. Shabat, Methods of the Theory of Function of Complex Variable (Nauka, Moscow, 1987) [in Russian].Google Scholar
  8. 8.
    N. R. Abubakirov and L. A. Aksent’ev, “Finite solutions to the inverse problem of the logarithmic potential,” Russ. Math. 60 (10), 55–58 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    V. K. Ivanov, Selected Scientific Papers (Fizmatlit, Moscow, 2008) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.N. I. Lobachevskii Institute of Mathematics and MechanicsKazan (Volga Region) Federal UniversityKazan, TatarstanRussia

Personalised recommendations