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Mat. Sb. (N.S.), 1973, Volume 90(132), Number 4, Pages 592–606 (Mi msb3068)  

This article is cited in 12 scientific papers (total in 13 papers)

On the analyticity of solutions of linear partial differential equations

O. A. Oleinik, E. V. Radkevich

Abstract: We study partial differential equations and systems all of whose solutions are analytic, and obtain a priori estimates on the analytic continuations of these solutions to the complex plane. Using these estimates, we obtain conditions which are necessary for the analyticity of all solutions of linear differential equations and systems with analytic coefficients.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 19:4, 581–596

Bibliographic databases:

UDC: 517.945
MSC: Primary 35B99; Secondary 35B45
Received: 02.10.1972

Citation: O. A. Oleinik, E. V. Radkevich, “On the analyticity of solutions of linear partial differential equations”, Mat. Sb. (N.S.), 90(132):4 (1973), 592–606; Math. USSR-Sb., 19:4 (1973), 581–596

Citation in format AMSBIB
\by O.~A.~Oleinik, E.~V.~Radkevich
\paper On~the analyticity of solutions of linear partial differential equations
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 4
\pages 592--606
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 4
\pages 581--596

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    This publication is cited in the following articles:
    1. O. A. Oleinik, E. V. Radkevich, “Ob odnom klasse lineinykh differentsialnykh uravnenii, imeyuschikh neanaliticheskie resheniya”, UMN, 28:3(171) (1973), 191–192  mathnet  mathscinet  zmath
    2. O. A. Oleinik, E. V. Radkevich, “Otsenki dlya sobstvennykh funktsii i reshenii nekotorykh sistem uravnenii s chastnymi proizvodnymi, zavisyaschikh ot parametra”, UMN, 28:4(172) (1973), 223–224  mathnet  mathscinet  zmath
    3. O. A. Oleinik, E. V. Radkevich, “O povedenii na beskonechnosti reshenii nekotorykh sistem uravnenii s chastnymi proizvodnymi”, UMN, 28:5(173) (1973), 249–250  mathnet  mathscinet  zmath
    4. O. A. Oleinik, E. V. Radkevich, “Ob usloviyakh analitichnosti vsekh reshenii lineinogo uravneniya vtorogo poryadka”, UMN, 29:3(177) (1974), 221–222  mathnet  mathscinet  zmath
    5. M. D. Bronshtein, “O differentsialnykh uravneniyakh, imeyuschikh neanaliticheskie resheniya”, UMN, 30:1(181) (1975), 227–228  mathnet  mathscinet  zmath
    6. Bernard Helffer, “Conditions ne´cessaires d'hypoanalyticite´pour des ope´rateurs invariantsa`gauche homoge`nes sur un groupe nilpotent gradue´”, Journal of Differential Equations, 44:3 (1982), 460  crossref
    7. 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
    8. I. E. Egorov, “Analyticity of solutions of singular elliptic equationns”, Math. USSR-Sb., 61:1 (1988), 147–153  mathnet  crossref  mathscinet  zmath
    9. Todor Gramchev, Petar Popivanov, Massafumi Yoshino, “Critical Gevrey index for hypoellipticity of parabolic operators and Newton polygones”, Annali di Matematica, 170:1 (1996), 103  crossref  mathscinet  zmath  isi
    10. Danilov V., Omel'yanov G., Radkevich E., “Hugoniot-Type Conditions and Weak Solutions to the Phase-Field System”, Eur. J. Appl. Math., 10:Part 1 (1999), 55–77  crossref  isi
    11. Sagun Chanillo, Bernard Helffer, Ari Laptev, “Nonlinear eigenvalues and analytic hypoellipticity”, Journal of Functional Analysis, 209:2 (2004), 425  crossref
    12. Gregorio Chinni, “Gevrey regularity for a generalization of the Oleǐnik–Radkevič operator”, Journal of Mathematical Analysis and Applications, 2013  crossref
    13. Sabir Umarov, “Pseudo-differential operators with meromorphic symbols and systems of complex differential equations”, Complex Variables and Elliptic Equations, 2014, 1  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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