We exhibit a canonical, finite dimensional solution family to certain singular SPDEs of the form \begin{ equation} \left(\partial_t- \sum_{ i,j=1}^d a_{ i,j}(x,t) \partial_i \partial_j - \sum_{ i=1}^d b_i(x,t) \partial_i - c(x,t)\right) u = F(u, \partial u, \xi) \ , \end{ equation} where $a_{ i,j}, b_i, c: \mathbb{ T}^d\times \mathbb{ R} \to \mathbb{ R}$ and $A=\{ a_{ i,j}\}_{ i,j=1}^d$ is uniformly elliptic. More specifically, we solve the non-translation invariant g-PAM, $\phi^4_2$, $\phi^4_3$ and KPZ-equation and show that the diverging renormalisation-functions are local functions of $A$. We also establish a continuity result for the solution map with respect to the differential operator for these equations.
Categories: math.AP math.PR