Pré-Publication, Document De Travail Année : 2025

Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness.

Résumé

We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough diffusion coefficients or kernels. Our results cover the Cauchy problem and allow a broad class of source terms under minimal assumptions. The core of the analysis is a set of sharp kinetic embeddings \`a la Lions and transfer-of-regularity results \`a la Bouchut--H\"ormander. We formulate these tools in a homogeneous, scale-invariant form, available for a large range of regularity parameters.

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Dates et versions

hal-04519638 , version 1 (25-03-2024)
hal-04519638 , version 2 (07-04-2024)
hal-04519638 , version 3 (05-12-2025)

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Pascal Auscher, Cyril Imbert, Lukas Niebel. Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness.. 2025. ⟨hal-04519638v3⟩
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