Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations 1FKS In her skillful re-engagement with

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Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations 1FKS In her skillful re-engagement withIn this paper, we 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, we establish the smooth joint density at multiple points. The tool we use is Malliavin calculus. The main ingredient is to prove that the solutions to a related stochastic