Regularity of the density for the stochastic heat equation

This is the published version, also available here: http://dx.doi.org/10.1214/EJP.v13-589.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