标题： 具有L{é}vy噪声的临界SPDE的扩展变分设置 显示英文标题

标题： An extended variational setting for critical SPDEs with L{é}vy noise

摘要： 临界变分设置最近被引入，并被证明适用于许多经典变分设置无法涵盖的重要随机偏微分方程（SPDEs）。 在本文中，我们以几种方式扩展了临界变分设置。 我们为非线性漂移项的范围空间引入了一种灵活性，因此某些临界情况现在也可以被包括在内。 一个例子是在弱设置下二维的Allen-Cahn方程。 此外，我们允许漂移在时间上是奇异的，这在研究SPDEs的大偏差原理的骨架方程时自然会出现。 最后但同样重要的是，我们展示了在Lévy噪声情况下的理论，而临界设置在此前尚未可用。 显示英文摘要

摘要： The critical variational setting was recently introduced and shown to be applicable to many important SPDEs not covered by the classical variational setting. In this paper, we extend the critical variational setting in several ways. We introduce a flexibility in the range space for the nonlinear drift term, due to which certain borderline cases can now also be included. An example of this is the Allen-Cahn equation in dimension two in the weak setting. In addition to this, we allow the drift to be singular in time, which is something that naturally arises in the study of the skeleton equations for large deviation principles for SPDEs. Last but not least, we present the theory in the case of L{\'e}vy noise for which the critical setting was not available yet.