A chain rule for a class of evolutive nonlocal hypoelliptic equations

Federico Buseghin; Nicola Garofalo

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arXiv · 1910.08803

A chain rule for a class of evolutive nonlocal hypoelliptic equations

Federico Buseghin·Nicola Garofalo

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Abstract

We prove a chain rule of local type for a class of fractional hypoelliptic equations of Kolmogorov-Fokker-Planck type. We introduce a semigroup based notion of nonlocal \emph{carré du champ} which works successfully in situations in which the infinitesimal generator of the semigroup itself does not necessarily possess a gradient. Our results extend and sharpen the original 2004 chain rule due to A. Córdoba and D. Córdoba.

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Federico Buseghin, Nicola Garofalo. 2019-10-19. A chain rule for a class of evolutive nonlocal hypoelliptic equations. https://arxiv.org/abs/1910.08803

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