A gradient estimate for the heat semi-group without hypoellipticity assumptions

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JournalProceedings of the American Mathematical Society
DatePublished - 1 Jan 2015
Issue number11
Volume143
Number of pages6
Pages (from-to)4967-4972
Original languageEnglish

Abstract

We obtain an estimate for the L<sup>p</sup> norm of the gradient of the heat semi-group in terms of the L<sup>p</sup> norm of the gradient. Our estimates are uniform for small times and p ∈ [1,∞]. The bounds only require some basic smoothness assumptions on the vector fields defining the diffusion underlying the problem.

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