We prove several pointwise estimates for solutions of linear parabolic equations with measurable coefficients in smooth cylinders through the weighted Ld+1-norm of the free term. The weights allow the free term to blow up near the lateral boundary. These are the first such results for parabolic equations with measurable coefficients. We also present the corresponding weighted estimates for occupation times of diffusion processes.
|Original language||English (US)|
|Number of pages||17|
|Journal||Journal of Mathematical Sciences (United States)|
|State||Published - Jan 1 2020|