We develop a solution theory in Hölder spaces for a quasi-linear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE lemmas which establish a priori Hölder bounds for a parabolic equation in divergence form with irregular right-hand-side term. We apply these bounds to the case of a right-hand-side noise term which is white in time and trace class in space, to obtain stretched exponential bounds for the Hölder semi-norms of the solution.

中文翻译：

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散度形式的准线性SPDE

我们在Hölder空间中开发了一种由加性噪声驱动的准​​线性随机PDE的解决方案理论。关键因素是两个确定性的PDE引理，它们为具有不规则右手边项的发散形式的抛物方程建立先验Hölder界。我们将这些边界应用于右侧噪声项的情况，该项在时间上是白色的，在空间上是迹线类的，以获得解的Hölder半范数的拉伸指数范围。