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On the Generalized Liouville Theorem

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Analysis, Probability, Applications, and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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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.

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References

  1. I. Vekua, Generalized Analytic Functions (Pergamon, Oxford, 1962)

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  2. V.S. Vinogradov, Liouville’s theorem for generalized analytic functions. Dokl. Akad. Nauk. SSSR 183(3), 500–508 (1968, in Russian)

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  3. G. Makatsaria, Liouville-type theorems for generalized analytic functions. Bull. Acad. Sci. Georgian SSR 113(3), 485–488 (1984)

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  4. 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)

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  5. R.P. Gilbert, J.L. Buchanan, First Order Elliptic Systems: A Function Theoretic Approach (Academic, Cambridge, 1983)

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Author information

Authors and Affiliations

  1. Ilia State University, Tbilisi, Georgia

    Nino Manjavidze

  2. St. Andrew the First Called Georgian University, Tbilisi, Georgia

    George Makatsaria

  3. Georgian Technical University, Tbilisi, Georgia

    Tamaz Vekua

  4. I. Vekua Institute of Applied Mathematics of Tbilisi State University, Tbilisi, Georgia

    George Akhalaia

Authors
  1. Nino Manjavidze
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  2. George Makatsaria
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  3. Tamaz Vekua
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  4. George Akhalaia
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Corresponding author

Correspondence to Nino Manjavidze .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Karl‐Olof Lindahl

  2. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Torsten Lindström

  3. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

  5. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Patrik Wahlberg

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Cite this paper

Manjavidze, N., Makatsaria, G., Vekua, T., Akhalaia, G. (2019). On the Generalized Liouville Theorem. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_11

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