On the theory of the Kolmogorov operator in the spaces $L^p$ and $C_{\infty }.$ I

Abstract

We obtain the basic results concerning the problem of constructing operator realizations of the formal differential expression $\nabla \cdot a\cdot \nabla -b\cdot \nabla$ with measurable matrix $a$ and vector field $b$ having critical-order singularities as the generators of Markov semigroups in $L^p$ and $C_{\infty }$.

arXiv comment61 p