Pejman Mahboubi
Published 2011-09-13, updated 2011-09-14Version 2
We study the smoothness of the density of the solution to the nonlinear heat equation u_t=Lu(t,x)+\sigma(u(t,x))W on a torus with a periodic boundary condition, where L is the generator of a Levy process on the torus, and W is white noise. We use Malliavin calculus techniques to show that the law of the solution has a density with respect to the Lebesgue measure for all t >0 and x in R.
Regularity of the density for the stochastic heat equation
A counterexample to maximal $L_p$-regularity of the stochastic heat equation in polygons: the case $p>4$
Regularity and strict positivity of densities for the stochastic heat equation on $\mathbb{R}^d$
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