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Mat. Sb. (N.S.), 1974, Volume 95(137), Number 1(9), Pages 130–145 (Mi msb3747)  

This article is cited in 8 scientific papers (total in 9 papers)

Analyticity and theorems of Liouville and Phragmén–Lindelöf type for general elliptic systems of differential equations

O. A. Oleinik, E. V. Radkevich


Abstract: Certain theorems on the analyticity of solutions of elliptic equations are used to prove theorems on the behavior of solutions of general elliptic systems of differential equations in unbounded regions, analogous to the classical theorems of Liouville and Phragmén–Lindelöf for harmonic functions. Theorems on the uniqueness of the solutions for elliptic boundary-value problems are also proved.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 24:1, 127–143

Bibliographic databases:

UDC: 517.946.82
MSC: 35B99, 35J55, 35B45
Received: 21.03.1974

Citation: O. A. Oleinik, E. V. Radkevich, “Analyticity and theorems of Liouville and Phragmén–Lindelöf type for general elliptic systems of differential equations”, Mat. Sb. (N.S.), 95(137):1(9) (1974), 130–145; Math. USSR-Sb., 24:1 (1974), 127–143

Citation in format AMSBIB
\Bibitem{OleRad74}
\by O.~A.~Oleinik, E.~V.~Radkevich
\paper Analyticity and theorems of Liouville and Phragm\'en--Lindel\"of type for general elliptic systems of differential equations
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 95(137)
\issue 1(9)
\pages 130--145
\mathnet{http://mi.mathnet.ru/msb3747}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=372418}
\zmath{https://zbmath.org/?q=an:0306.35045}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 24
\issue 1
\pages 127--143
\crossref{https://doi.org/10.1070/SM1974v024n01ABEH001908}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. S. Soboleva, “O nekotorykh svoistvakh reshenii ellipticheskikh uravnenii vtorogo poryadka v neogranichennykh oblastyakh”, UMN, 31:5(191) (1976), 253–254  mathnet  mathscinet  zmath
    2. V. M. Miklyukov, “On the asymptotic properties of subsolutions of quasilinear equations of elliptic type and mappings with bounded distortion”, Math. USSR-Sb., 39:1 (1981), 37–60  mathnet  crossref  mathscinet  zmath  isi
    3. A. M. Il'in, E. F. Lelikova, “Asymptotics of solutions of some elliptic equations in unbounded domains”, Math. USSR-Sb., 47:2 (1984), 295–313  mathnet  crossref  mathscinet  zmath
    4. Tedeev A., Shishkov A., “Behavior of Solutions of Quasi-Linear Elliptical Equations in Unbounded-Domains”, no. 9, 1984, 23–26  isi
    5. V. I. Arnol'd, M. I. Vishik, I. M. Gel'fand, Yu. V. Egorov, A. S. Kalashnikov, A. N. Kolmogorov, S. P. Novikov, S. L. Sobolev, “Ol'ga Arsen'evna Oleinik (on her sixtieth birthday)”, Russian Math. Surveys, 40:5 (1985), 267–287  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Levin B. Kheifets A., “Asymptotic-Behavior of Subfunctions of the Schrodinger Operator in a N-Dimensional Cone”, 301, no. 3, 1988, 540–543  isi
    7. V. M. Miklyukov, “Stagnation Zones of Solutions to the Laplace–Beltrami Equation in Long Strips”, Siberian Adv. Math., 12:3 (2002), 62–78  mathnet  mathscinet  zmath  elib
    8. A. R. Gerfanov, F. Kh. Mukminov, “Shirokii klass edinstvennosti resheniya dlya neravnomerno ellipticheskogo uravneniya v neogranichennoi oblasti”, Ufimsk. matem. zhurn., 1:3 (2009), 11–27  mathnet  zmath  elib
    9. V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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