Note on smoothing estimates for Kolmogorov type equations

Yasunori Maekawa ()
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Yasunori Maekawa: Kyoto University

Partial Differential Equations and Applications, 2021, vol. 2, issue 6, 1-12

Abstract: Abstract In this paper we give the weighted $$L^2$$ L 2 estimate for the solution to the Kolmogorov type equations, where the classical Vlasov-Fokker-Planck equation and the heat with a drift term by the shear flows are contained as the typical examples. Our estimate gives the classical smoothing rate of the order $$\frac{2}{3}$$ 2 3 in a suitable weighted norm.

Keywords: Hypoelliptic estimate; Kolmogorov equations; 35B65; 35H10; 35K10; 35Q35 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00135-2

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