On the gradient estimates for evolution operators associated to Kolmogorov operators

TL;DR

This paper establishes sufficient conditions for pointwise gradient estimates of evolution operators linked to nonautonomous second order parabolic operators, and identifies a class of operators meeting these conditions.

Contribution

It provides new criteria for gradient estimates and demonstrates a class of operators that satisfy these criteria, advancing understanding of evolution operators with unbounded coefficients.

Findings

Established sufficient conditions for gradient estimates.

Identified a class of operators satisfying these conditions.

Enhanced understanding of evolution operators with unbounded coefficients.

Abstract

We determine sufficient conditions for the occurrence of a pointwise gradient estimate for the evolution operators associated to nonautonomous second order parabolic operators with (possibly) unbounded coefficients. Moreover we exhibit a class of operators which satisfy our conditions.