We consider a degenerate Kolmogorov-Fokker-Planck operator in non-divergence form bounded measurable coefficients. We assume that the drift term is a linear function of the space variable that makes hypoelliptic the corresponding operator with constant coefficients. We construct an explicit fundamental solution Γ for L, study its properties, show a comparison result between Γ and the fundamental solution of some model operators with constant coefficients, and show the unique solvability of the Cauchy problem for L under various assumptions on the initial datum.

Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients / Bramanti, Marco; Polidoro, Sergio. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 2:4(2020), pp. 734-771. [10.3934/mine.2020035]

Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients

Polidoro, Sergio
Writing – Original Draft Preparation
2020

Abstract

We consider a degenerate Kolmogorov-Fokker-Planck operator in non-divergence form bounded measurable coefficients. We assume that the drift term is a linear function of the space variable that makes hypoelliptic the corresponding operator with constant coefficients. We construct an explicit fundamental solution Γ for L, study its properties, show a comparison result between Γ and the fundamental solution of some model operators with constant coefficients, and show the unique solvability of the Cauchy problem for L under various assumptions on the initial datum.
2020
10-lug-2020
2
4
734
771
Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients / Bramanti, Marco; Polidoro, Sergio. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 2:4(2020), pp. 734-771. [10.3934/mine.2020035]
Bramanti, Marco; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1225931
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