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).
Lax type formulas with lower semicontinuous initial data and hypercontractivity results / Antonio, Avantaggiati; Loreti, Paola. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 20:3(2013), pp. 385-411. [10.1007/s00030-012-0157-2]
Lax type formulas with lower semicontinuous initial data and hypercontractivity results
LORETI, Paola
2013
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
