Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations - Le Chen - Bog

In this paper, the authors establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone condition for the diffusion coefficient, they establish the smooth joint density at multiple points.