On the fundamental solution for degenerate Kolmogorov equations with rough coefficients

TL;DR

This paper establishes the existence of a fundamental solution for degenerate Kolmogorov equations with rough coefficients, providing Gaussian bounds and analyzing its properties in the dilation invariant setting.

Contribution

It proves the existence and Gaussian bounds of the fundamental solution for Kolmogorov equations with measurable, rough coefficients, extending classical results to degenerate cases.

Findings

Existence of a fundamental solution for the equation.

Gaussian upper and lower bounds established.

Properties of the fundamental solution analyzed.

Abstract

The aim of this work is to prove the existence of a fundamental solution associated to the Kolmogorov equation L u = f with measurable coefficients in the dilation invariant case. Moreover, we prove Gaussian upper and lower bounds for it, and other related properties.