Published January 1, 2004
| Version v1
Journal article
Open
Nonlinear diffusions, hypercontractivity and the optimal $L\sp p$-Euclidean logarithmic Sobolev inequality
Creators
Description
The equation ut = ∆p(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.
Files
article.pdf
Files
(249.4 kB)
Name | Size | Download all |
---|---|---|
md5:034ab554d06a275a7aefbb44fc27f78c
|
249.4 kB | Preview Download |