Weighted Aleksandrov estimates: PDE and stochastic versions

Abstract

We prove several pointwise estimates for solutions of linear elliptic (parabolic) equations with measurable coefficients in smooth domains (cylinders) through the weighted $L_d$ ($L_{d+1}$)-norm of the free term. The weights allow the free term to blow up near the (latteral) boundary. We also present weighted estimates for occupation times of diffusion processes.

27 pages