On Diffusion Processes with Drift in Ld+ 1

This paper is a natural continuation of Krylov (2020 and 2021) where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded nondegenerate diffusion drift $L_{d+1}(\mathbb {R}^{d+1})$ some properties their Green’s functions probability passing through narrow tubes investigated. On the basis this here we study further these such as Harnack inequality, Hölder continuity potentials, Fanghua Lin estimates so on.