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Journal articles
Hamilton Jacobi equations on metric spaces and transport-entropy inequalities
Abstract : We prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton- Jacobi equations on a general metric space. As a rst consequence, we show in full generality that the log-Sobolev inequality is equivalent to an hypercontractivity property of the Hamilton-Jacobi semi-group. As a second consequence, we prove that Talagrand's transportentropy inequalities in metric space are characterized in terms of log-Sobolev inequalities restricted to the class of c-convex functions.
https://hal-upec-upem.archives-ouvertes.fr/hal-00795829
Contributor : Nathael Gozlan <>
Submitted on : Friday, March 1, 2013 - 2:46:06 AM
Last modification on : Tuesday, March 2, 2021 - 10:14:39 AM
Long-term archiving on: : Thursday, May 30, 2013 - 4:00:26 AM
Contributor : Nathael Gozlan <>
Submitted on : Friday, March 1, 2013 - 2:46:06 AM
Last modification on : Tuesday, March 2, 2021 - 10:14:39 AM
Long-term archiving on: : Thursday, May 30, 2013 - 4:00:26 AM
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HJ-revised.pdf
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