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.
Citation:
O. A. Oleinik, E. V. Radkevich, “Analyticity and theorems of Liouville and Phragmén–Lindelöf type for general elliptic systems of differential equations”, Math. USSR-Sb., 24:1 (1974), 127–143
\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 Math. USSR-Sb.
\yr 1974
\vol 24
\issue 1
\pages 127--143
\mathnet{http://mi.mathnet.ru/eng/sm3747}
\crossref{https://doi.org/10.1070/SM1974v024n01ABEH001908}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=372418}
\zmath{https://zbmath.org/?q=an:0306.35045}
Linking options:
https://www.mathnet.ru/eng/sm3747
https://doi.org/10.1070/SM1974v024n01ABEH001908
https://www.mathnet.ru/eng/sm/v137/i1/p130
This publication is cited in the following 10 articles:
V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71
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
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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
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vtorogo poryadka v neogranichennykh oblastyakh”, UMN, 31:5(191) (1976), 253–254
Citation in format AMSBIB
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