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Lax type formulas with lower semicontinuous initial data and hypercontractivity results

Abstract : In Avantaggiati and Loreti [Ric. Mat. 57(2):171-202, 2008] we studied the Cauchy problem for a class of Hamilton-Jacobi equations with initial data verifying the Lipschitz condition. In this paper we extend those results to the case in which the initial data are lower semicontinuous [in the following lsc], and are lower bounded and semiconvex. Here we prove hypercontractivity results and new Logarithm Sobolev Inequalities (shortly, LSI).
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https://hal.inria.fr/hal-00724777
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, August 22, 2012 - 3:52:34 PM
Last modification on : Sunday, March 29, 2020 - 6:22:03 PM

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Antonio Avantaggiati, Paola Loreti. Lax type formulas with lower semicontinuous initial data and hypercontractivity results. Nonlinear Differential Equations and Applications, Springer Verlag, 2012, ⟨10.1007/s00030-012-0157-2⟩. ⟨hal-00724777⟩

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