Optimal Holder regularity for nonautonomous Kolmogorov equations

TL;DR

This paper establishes optimal Schauder estimates for solutions to nonautonomous Kolmogorov equations with unbounded coefficients, advancing the understanding of regularity in parabolic PDEs.

Contribution

It provides the first optimal Schauder estimates for nonautonomous elliptic operators with unbounded coefficients in a parabolic setting.

Findings

Proved optimal Schauder estimates for solutions.

Extended regularity results to nonautonomous operators.

Applicable to a broad class of unbounded coefficient operators.

Abstract

We consider a class of nonautonomous elliptic operators ${\mathscr A}$ with unbounded coefficients defined in $[0,T]\times\R^N$ and we prove optimal Schauder estimates for the solution to the parabolic Cauchy problem $D_tu={\mathscr A}u+f$, $u(0,\cdot)=g$.