Journal
POTENTIAL ANALYSIS
Volume 48, Issue 2, Pages 125-157Publisher
SPRINGER
DOI: 10.1007/s11118-017-9628-8
Keywords
Hamilton-Jacobi equations; Weak-transport entropy inequalities; Modified Log-Sob inequalities on graphs
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This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity of this class of infimal-convolution operators is connected to some discrete version of the log-Sobolev inequality and to a discrete version of Talagrand's transport inequality.
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