Global Properties of Transition Probabilities of Singular Diffusions
Giorgio Metafune, Diego Pallara, Abdelaziz Rhandi · Theory of Probability and Its Applications · 2010
We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order differential operators in ${\bf R}^N$ with unbounded drift. As an application, we obtain sufficient conditions implying the differentiability of the associated transition semigroup on the space of bounded and continuous functions on ${\bf R}^N$.