# Gaussian lower bounds for non-homogeneous Kolmogorov equations with measurable coefficients

## TL;DR

This paper establishes Gaussian lower and upper bounds for fundamental solutions of certain degenerate parabolic equations with measurable coefficients, extending classical results to non-homogeneous, weakly hypoelliptic cases.

## Contribution

It provides Gaussian bounds for degenerate Kolmogorov equations with measurable coefficients, generalizing classical uniform parabolic results.

## Key findings

- Gaussian bounds are independent of coefficient smoothness
- Bounds apply to weak Hörmander condition equations
- Extends classical results to non-homogeneous cases

## Abstract

We prove Gaussian upper and lower bounds for the fundamental solutions of a class of degenerate parabolic equations satisfying a weak Hormander condition. The bound is independent of the smoothness of the coefficients and generalizes classical results for uniformly parabolic equations