On diffusion processes with drift in $L_{d+1}$

Abstract

This paper is a natural continuation of \cite{Kr_20_2} and \cite{Kr_21_1} where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}(\mathbb{R}^{d+1})$ and some properties of their Green's functions and probability of passing through narrow tubes are investigated. On the basis of this here we study some further properties of these processes such as Harnack inequality, H\"older continuity of potentials, Fanghua Lin estimates and so on.