ON ESTIMATES OF THE MAXIMUM OF A SOLUTION OF A PARABOLIC EQUATION AND ESTIMATES OF THE DISTRIBUTION OF A SEMIMARTINGALE

Abstract

Estimates are proved for the maximum of a solution of a linear parabolic equation in terms of the -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 -estimates are proved also for the distributions of semimartingales.Bibliography: 16 titles.