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October 2001 Cahn-Hilliard stochastic equation: existence of the solution and of its density
Caroline Cardon-Weber
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Bernoulli 7(5): 777-816 (October 2001).


We show the existence and uniqueness of a function-valued process solution to the stochastic Cahn-Hilliard equation driven by space-time white noise with a nonlinear 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.


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Caroline Cardon-Weber. "Cahn-Hilliard stochastic equation: existence of the solution and of its density." Bernoulli 7 (5) 777 - 816, October 2001.


Published: October 2001
First available in Project Euclid: 15 March 2004

zbMATH: 0995.60058
MathSciNet: MR2002I:60109

Keywords: Cahn-Hilliard equation , Green function , Malliavin calculus , Stochastic partial differential equations

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

Vol.7 • No. 5 • October 2001
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