# Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients

## TL;DR

This paper establishes local boundedness of solutions to certain degenerate Kolmogorov equations with measurable coefficients, even with minimal assumptions on lower order terms, advancing understanding of their regularity.

## Contribution

It provides new Moser-type estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients under minimal integrability conditions.

## Key findings

- Solutions are locally bounded despite degeneracy and minimal coefficient regularity.
- The results extend regularity theory for Kolmogorov equations with less restrictive assumptions.
- Methodology involves novel adaptations of Moser's iteration technique.

## Abstract

We prove the local boundedness of the solutions to degenerate second order partial differential equations of Kolmogorov type with measurable coefficients in divergence form, under minimal integrability assumption on the lower order coefficients.