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On an Aleksandrov-Bakel’man type maximum principle for second-order parabolic equations. (English) Zbl 0581.35027
This paper presents an exact analogue, for second order linear parabolic equations, of the maximum principle for elliptic equations of A. D. Aleksandrov [Vestn. Leningr. Univ., Mat. Mekh. Astron. 21, Nr. 1, 5-25 (1966; Zbl 0146.34702)] and I. Ya. Bakel’man [Sib. Mat. Zh. 2, 179- 186 (1961; Zbl 0100.30503)]. The result is an improvement, in several ways, of a theorem of N. V. Krylov [Sib. Math. J. 17, 226-236 (1976); translation of Sib. Mat. Zh. 17, 290-303 (1976; Zbl 0354.35052)].
Reviewer: N.A.Watson

MSC:
35K15 Initial value problems for second-order parabolic equations
35B50 Maximum principles in context of PDEs
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References:
[1] Aleksandrov A.D., English translation in AMS Transl.(2) 68 pp 120– (1968)
[2] I.Ya. Bakel’man, Siberian Math. J. 2 pp 179– (1961)
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