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- W2232179903 abstract "We derive the hypoelliptic estimates for a kinetic equation of the form where d ≥ 1, β ≥0, 𝕊d is the unit sphere in ℝd+1 and Δd is the Laplace-Beltrami operator on 𝕊d. Such equations arise in the modeling of high frequency waves in random media with long-range correlations. Assuming some (fractional) Sobolev regularity in the momentum variable k ∈ 𝕊d, we obtain estimates for the fractional derivatives of f in the (t, x) variables. Our proof follows the method of Bouchut based on the regularization of the momentum variable and on averaging lemmas on the sphere." @default.
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- W2232179903 date "2015-10-30" @default.
- W2232179903 modified "2023-10-10" @default.
- W2232179903 title "Hypoelliptic estimates in radiative transfer" @default.
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- W2232179903 doi "https://doi.org/10.1080/03605302.2015.1096287" @default.
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