标题： 非平移不变奇异SPDE的经典解 显示英文标题

标题： Canonical solutions to non-translation invariant singular SPDEs

摘要： 我们展示了一类特定的奇异SPDEs的规范的、有限维的解族，形式为\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}，其中$a_{i,j}, b_i, c: \mathbb{T}^d\times \mathbb{R} \to \mathbb{R}$和$A=\{a_{i,j}\}_{i,j=1}^d$是均匀椭圆的。 更具体地说，我们求解了非平移不变的g-PAM，$\phi^4_2$，$\phi^4_3$和KPZ方程，并表明发散的重整化函数是$A$的局部函数。 我们还建立了这些方程的解映射相对于微分算子的连续性结果。 显示英文摘要

摘要： 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.