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On the Generalized Liouville Theorem

  • Nino ManjavidzeEmail author
  • George Makatsaria
  • Tamaz Vekua
  • George Akhalaia
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper a generalization of the classical Liouville theorem for the solutions of special type elliptic systems and some nonclassical interpretations of this theorem are obtained.

References

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    I. Vekua, Generalized Analytic Functions (Pergamon, Oxford, 1962)zbMATHGoogle Scholar
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    V.S. Vinogradov, Liouville’s theorem for generalized analytic functions. Dokl. Akad. Nauk. SSSR 183(3), 500–508 (1968, in Russian)Google Scholar
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    G. Makatsaria, Liouville-type theorems for generalized analytic functions. Bull. Acad. Sci. Georgian SSR 113(3), 485–488 (1984)MathSciNetGoogle Scholar
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    A.L. Goncharov, S.B. Klimentov, Z.D. Usmanov, An analogue of Liouville’s theorem for a class of systems of Cauchy–Riemann type with singular coefficients. Vladikavkaz. Mat. Zh. 7(4), 7–16 (2005, in Russian)Google Scholar
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    R.P. Gilbert, J.L. Buchanan, First Order Elliptic Systems: A Function Theoretic Approach (Academic, Cambridge, 1983)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nino Manjavidze
    • 1
    Email author
  • George Makatsaria
    • 2
  • Tamaz Vekua
    • 3
  • George Akhalaia
    • 4
  1. 1.Ilia State UniversityTbilisiGeorgia
  2. 2.St. Andrew the First Called Georgian UniversityTbilisiGeorgia
  3. 3.Georgian Technical UniversityTbilisiGeorgia
  4. 4.I. Vekua Institute of Applied Mathematics of Tbilisi State UniversityTbilisiGeorgia

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