Existence and regularity of the density for solutions of stochastic differential equations with boundary noise

We study the existence and regularity of densities for the solution of a nonlinear heat diffusion with stochastic perturbation of Brownian and fractional Brownian motion type: we use the Malliavin calculus in order to prove that, if the nonlinear term is suitably regular, then the law of the solution has a smooth density with respect to the Lebesgue measure