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We study existence and regularity of the density for the solution $u(t,x)$(with fixed $t > 0$ and $x \in D$) of the heat equation in a bounded domain $D\subset \mathbb R^d$ driven by a stochastic inhomogeneous Neumann boundarycondition with stochastic term. The stochastic perturbation is given by afractional Brownian motion process. Under suitable regularity assumptions onthe coefficients, by means of tools from the Malliavin calculus, we prove thatthe law of the solution has a smooth density with respect to the Lebesguemeasure in $\mathbb R$.

Absolute continuity of the law for solutions of stochastic differential equations with boundary noise