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


Authors: Thomas Cass and Christian Litterer
Journal: Proc. Amer. Math. Soc. 143 (2015), 4967-4972
MSC (2010): Primary 60H30; Secondary 60J60
DOI: https://doi.org/10.1090/proc/12582
Published electronically: July 14, 2015
MathSciNet review: 3391053
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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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Additional Information

Thomas Cass
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: thomas.cass@imperial.ac.uk

Christian Litterer
Affiliation: Centre de Mathématiques Appliquées, École Polytechnique, Route de Saclay, 91128 Palaiseau, France
Email: christian.litterer@gmail.com

DOI: https://doi.org/10.1090/proc/12582
Received by editor(s): December 28, 2013
Received by editor(s) in revised form: June 22, 2014
Published electronically: July 14, 2015
Additional Notes: The research of the second author has received support from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 321111.
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2015 American Mathematical Society