Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : The equation ut =Dp (u1/(p1)) 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 LpEuclidean 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 LpEuclidean logarithmic Sobolev inequality. A large deviation result based on a HamiltonJacobi equation and also related to the LpEuclidean logarithmic Sobolev inequality is then stated. 





200239 

02122002 

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