Malliavin calculus for white noise driven parabolic SPDEs (Q1275362)

For an SPDE of the form \(\partial_t X=\partial^2_t X+\psi(X)+\varphi(X)\dot{W}\) with space time white noise \(W(t,x)\), \(x\in[0,1]\), and the Neumann boundary condition, the authors use the Malliavin calculus to prove that the law of \((X(t,x_1),\ldots,X(t,x_d))\), \(0\leq x_1<\ldots<x_d\), is absolutely continuous with respect to Lebesgue measure with strictly positive density, provided the coefficients \(\psi\), \(\varphi\) are infinitely differentiable with bounded derivatives of all orders.