We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation.
Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift / Anceschi, F.; Ascione, G.; Castorina, D.; Solombrino, F.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 543:2(2025). [10.1016/j.jmaa.2024.128909]
Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
Anceschi F.;Castorina D.
;Solombrino F.
2025
Abstract
We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation.File in questo prodotto:
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