Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On strongly Petrovskii's parabolic SPDEs in arbitrary dimension


Code(s) de Classification MSC:

Résumé: In this paper we show that the Cahn-Hilliard stochastic SPDE has a function valued solution in dimension 4 and 5 when the perturbation is driven by a space-correlated Gaussian noise. This is done proving general results on SPDEs with globally Lipschitz coefficients associated with operators on smooth domains of $\mathbb{R}^d$ which are parabolic in the sense of Petrovski\u{\i}, and do not necessarily define a semi-group of operators. We study the regularity of the trajectories of the solutions and the absolute continuity of the law at some given time and position.

Mots Clés: Parabolic operators ; Cahn-Hilliard equation ; Green function ; SPDEs ; Malliavin calculus.

Date: 2001-09-17

Prépublication numéro: PMA-685

Postscript file : PMA-685.ps

Revised version (Oct 12 2001): PMA-685bis.ps, PMA-685bis.dvi