Pré-Publication, Document De Travail Année : 2012

On Harnack inequalities and optimal transportation

Résumé

We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation. Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is emphasized. Commutation properties between the heat and Hopf-Lax semigroups are developed consequently, providing direct access to the heat flow contraction property along Wasserstein distances.

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Dates et versions

hal-00742654 , version 1 (16-10-2012)
hal-00742654 , version 2 (17-10-2012)
hal-00742654 , version 3 (18-10-2012)
hal-00742654 , version 4 (25-10-2012)
hal-00742654 , version 5 (08-07-2013)

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Dominique Bakry, Ivan Gentil, Michel Ledoux. On Harnack inequalities and optimal transportation. 2012. ⟨hal-00742654v2⟩

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