On generalized Landis-type growth lemmas in application to second order parabolic equations

In our joint results with N.V. Krylov on the Holder and Harnack estimates for second order elliptic and parabolic equations, the treatment of parabolic equations required some additional steps. In the probabilistic interpretation, it was essential that the corresponding stochastic processes have constant drift along the time axis. We discuss how it is possible to extend these techniques to more general flows, regardless of their direction.