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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Nonlinear Differential Equations and Applications, Springer Verlag, 2012, 〈10.1007/s00030-012-0157-2〉
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Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 15:52:34
Dernière modification le : lundi 21 mars 2016 - 11:34:47

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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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