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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60H07 Stochastic calculus of variations and the Malliavin calculus
- 60H15 Stochastic partial differential equations, See also {35R60}
- 35R60 Partial differential equations with randomness, See Also {

**Résumé:** This article is devoted to show first the existence and
uniqueness of a function-valued process solution to the stochastic
Cahn-Hilliard equation driven by the space-time
white noise with a non-linear diffusion coefficient. Then we show that
the solution is locally differentiable in the sense of the Malliavin calculus,
and under some non-degeneracy condition on the diffusion coefficient
that,
the law of the solution is absolutely continuous with respect to Lebesgue
measure.

**Mots Clés:** *Cahn-Hilliard equation ; Green functions ; SPDEs ; Malliavin calculus*

**Date:** 1999-12-02

**Prépublication numéro:** *PMA-543*

**Revised version 2001-01-24 : **PMA-543bis.dvi