Lobachevskii Journal of Mathematics

, Volume 37, Issue 3, pp 231–233 | Cite as

A uniqueness theorem for linear elliptic equations with dominating derivative with respect to \(\bar z\)

  • I. A. Bikchantaev


The interior uniqueness theorem for analytic functions was generalized by M.B. Balk to the case of polyanalytic functions of order n. He proved that, if the zeros of a polyanalytic function have an accumulation point of order n, then this function is identically zero. M.F. Zuev generalized this result to the case of metaanalytic functions. In this paper, we generalize the interior uniqueness theorem to solutions of linear homogeneous elliptic differential equations of order n with analytic coefficients whose senior derivative is the n-th power of the Cauchy–Riemann operator.

Keywords and phrases

Elliptic equation the uniqueness theorem 


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  1. 1.
    I. A. Bikchantaev, Differential equations 47 (2), 278–282 (2011).MathSciNetCrossRefGoogle Scholar
  2. 2.
    I. A. Bikchantaev, Russian Mathematics (Iz. VUZ) 59 (5), 17–21 (2015).MathSciNetGoogle Scholar
  3. 3.
    M. B. Balk, Polyanalytic functions (Akademie Verlag, Berlin, 1991).MATHGoogle Scholar
  4. 4.
    I. A. Bikchantaev, Differential equations 50 (2), 217–222 (2014).MathSciNetCrossRefGoogle Scholar
  5. 5.
    F. John, Plane waves and spherical means applied to partial differential equations (Institute of mathematical sciences, New York University, 1955).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Kazan Federal UniversityKazanRussia

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