This article is cited in 21 papers

On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale

N. V. Krylov


Abstract: Estimates are proved for the maximum of a solution of a linear parabolic equation in terms of the $\mathscr L_p$-norm of the right-hand side. The coefficients of the first derivatives are assumed to be integrable to a suitable power. Various boundary value problems are considered. Corresponding $\mathscr L_p$-estimates are proved also for the distributions of semimartingales.
Bibliography: 16 titles.

UDC: 517.95

MSC: Primary 35K20, 60G48; Secondary 35B50, 60E99

Received: 10.06.1985

 English version: Mathematics of the USSR-Sbornik, 1987, 58:1, 207–221

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