On the fundamental solution for degenerate Kolmogorov equations with rough coefficients

Abstract

The aim of this work is to prove the existence of a fundamental solution associated to the Kolmogorov equation mathscr {L}u = f in the dilation invariant case, with bounded measurable first order coefficients and bounded diffusion coefficients satisfying a sort of divergence free assumption. Finally, we prove Gaussian upper and lower bounds for the fundamental solution, and other related properties, under less restrictive assumptions on the coefficients.