Differential Equations

, Volume 54, Issue 4, pp 476–485 | Cite as

Construction of a Carleman Function Based on the Tikhonov Regularization Method in an Ill-Posed Problem for the Laplace Equation

  • E. B. Laneev
Partial Differential Equations


Based on the Tikhonov regularization method, we explicitly construct a Carleman function in an ill-posed mixed problem for the Laplace equation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lavrent’ev, M.M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki (On Some Ill-Posed Problems of Mathematical Physics), Novosibirsk, 1962.Google Scholar
  2. 2.
    Goluzin, G.M. and Krylov, V.I., Generalized Carleman’s formulas, Mat. Sb., 1933, vol. 40, no. 2, pp. 144–149.Google Scholar
  3. 3.
    Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods for Solving Ill-Posed Problems), Moscow: Nauka, 1986.zbMATHGoogle Scholar
  4. 4.
    Ivanov, V.K., The Cauchy problem for the Laplace equation in an infinite strip, Differ. Equations, 1965, vol. 1, no. 1, pp. 98–102.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Glasko, V.B., Obratnye zadachi matematicheskoi fiziki (Inverse Problems of Mathematical Physics), Moscow: Mosk. Gos. Univ., 1984.zbMATHGoogle Scholar
  6. 6.
    Aizenberg, L.A., Formuly Karlemana v kompleksnom analize (Carleman’s Formulas in Complex Analysis), Novosibirsk: Nauka, 1990.Google Scholar
  7. 7.
    Shlapunov, A.A., On the Cauchy problem for the Laplace equation, Sib. Mat. Zh., 1992, vol. 33, no. 3, pp. 205–215.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Yarmukhamedov, Sh., A Carleman function and the Cauchy problem for the Laplace equation, Sib. Math. J., 2004, vol. 45, no. 3, pp. 580–595.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Prilepko, A.I., Inverse problems of potential theory, Math. Notes, 1973, vol. 14, no. 5, pp. 990–996. DIFFERENTIAL EQUATIONSCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations