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Regularity of the density for the stochastic heat equation

   
@article{EJP589,
	author = {Carl Mueller and David Nualart},
	title = {Regularity of the density for the stochastic heat equation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {heat equation, white noise, Malliavin calculus, stochastic partial differential equations.},
	abstract = {We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise.  Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise.  Then we settle this question by proving that solutions to the linear equation have negative moments of all orders.},
	pages = {no. 74, 2248-2258},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-589},    
        url = {http://ejp.ejpecp.org/article/view/589}}