Regularity of the density for a stochastic heat equation

Abstract: 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.