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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2012

Lax type formulas with lower semicontinuous initial data and hypercontractivity results

Résumé

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).

Dates et versions

hal-00724777 , version 1 (22-08-2012)

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