Carl Mueller, David Nualart
Published 2007-09-17Version 1
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.
Journal: Electronic J. Prob., 13, paper 74, 2248-2258, (2008)
Regularity of the density for a stochastic heat equation
Regularity and strict positivity of densities for the stochastic heat equation on $\mathbb{R}^d$
A counterexample to maximal $L_p$-regularity of the stochastic heat equation in polygons: the case $p>4$
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