Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : The equation ut =Dp (u1/(p-1)) for p>1 is a nonlinear generalization of the heat equation which is also homogeneous, of degree 1. For large time asymptotics, its links with the optimal Lp-Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focuse on the existence and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the Lp-Euclidean logarithmic Sobolev inequality. A large deviation result based on a Hamilton-Jacobi equation and also related to the Lp-Euclidean logarithmic Sobolev inequality is then stated.
 
 
NONLINEAR DIFFUSIONS, HYPERCONTRACTIVITY AND THE OPTIMAL LP-EUCLIDEAN LOGARITHMIC SOBOLEV INEQUALITY
DEL PINO Manuel, DOLBEAULT Jean, GENTIL Ivan
2002-39
02-12-2002
 
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
Téléphone : +33 (0)1 44-05-49-23 - fax : +33 (0)1 44-05-45-99