Geodesic
On~the analyticity of solutions of linear partial differential equations
Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 581-596

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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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     title = {On~the analyticity of solutions of linear partial differential equations},
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O. A. Oleinik; E. V. Radkevich. On~the analyticity of solutions of linear partial differential equations. Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 581-596. http://geodesic.mathdoc.fr/item/SM_1973_19_4_a4/