The aim of this work is to prove the existence of a fundamental solution associated to the Kolmogorov equation Lu= 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.
On the fundamental solution for degenerate Kolmogorov equations with rough coefficients
Anceschi F;
2023-01-01
Abstract
The aim of this work is to prove the existence of a fundamental solution associated to the Kolmogorov equation Lu= 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.
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