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We prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton- Jacobi equations on a general metric space.
Convex analysis
R. T. Rockafellar · 1970
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Logarithmic Sobolev inequalities
L. Gross · 1975
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A simple proof of the blowing-up lemma
K. Marton · 1986
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Theory of Orlicz spaces
M. M. Rao and Z. D. Ren · 1991
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Transportation cost for Gaussian and other product measures
M. Talagrand · 1996
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Partial differential equations
L. C. Evans · 1998
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Mass transportation problems. Vol. I
S. T. Rachev and L. Rüschendorf · 1998
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Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
S. G. Bobkov and F. Götze · 1999
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
F. Otto and C. Villani · 2000
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Hypercontractivity of Hamilton-Jacobi equations
S. G. Bobkov, I. Gentil, and M. Ledoux · 2001
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Probability distance inequalities on Riemannian manifolds and path spaces
F. Y. Wang · 2004
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Modified logarithmic Sobolev inequalities and transportation inequalities
I. Gentil, A. Guillin, and L. Miclo · 2005
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Hamilton-Jacobi semigroup on length spaces and applications
J. Lott and C. Villani · 2007
A characterization of dimension free concentration in terms of transport inequalities
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C. Villani · 2009
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L. Ambrosio, N. Gigli, and G. Savaré · 2011
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From log sobolev to talagrand: a quick proof
N. Gigli and M. Ledoux · 2011
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A new characterization of Talagrand’s transport-entropy inequalities and applications
N. Gozlan, C. Roberto, and P.M. Samson · 2011
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Density of lipschitz functions and equivalence of weak gradients in metric measure spaces
L. Ambrosio, N. Gigli, and G. Savaré · 2012
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Functional inequalities and Hamilton-Jacobi equations in geodesic spaces
Z. Balogh, A. Engoulatov, L. Hunziker, and O. E. Maasalo · 2009
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Characterization of Talagrand’s transport-entropy inequalities in metric spaces
N. Gozlan, C. Roberto, and P.M. Samson · 2012
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