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

Cass, Thomas; Litterer, Christian

doi:10.1090/proc/12582

A gradient estimate for the heat semi-group without hypoellipticity assumptions
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Proc. Amer. Math. Soc. 143 (2015), 4967-4972 Request permission

Abstract:

We obtain an estimate for the $L^{p}$ norm of the gradient of the heat semi-group in terms of the $L^{p}$ norm of the gradient. Our estimates are uniform for small times and $p\in \left [ 1,\infty \right ]$. The bounds only require some basic smoothness assumptions on the vector fields defining the diffusion underlying the problem.

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