Lions in Lions (1969) solved the anisotropic p-Laplace equation in deterministic setting by considering the anisotropic p-Laplace operator in d-dimensions as a sum of d monotone coercive operators each defined on a different space. Motivated by this example, we prove existence and uniqueness results for a large class of stochastic partial differential equations(SPDEs) driven by Lévy noise when the operator appearing in the bounded variation term is a sum of operators having different analytic and growth properties. Further, the operators are allowed to be locally monotone without explicitly restricting the growth of the operators appearing in the stochastic integrals. This has been done by identifying an appropriate coercivity condition. As a consequence, well-posedness of Lévy driven stochastic Anisotropic p-Laplace equation has been shown. Our framework is most general till date. Many popular SPDEs appearing in real world models such as the stochastic Ginzburg–Landau equation and stochastic Swift–Hohenberg equation, both driven by Lévy noise, fit in our setting. These equations are not covered by the corresponding results in the literature.

在狮子（1969）狮子解决了各向异性p通过考虑各向异性-Laplace方程中确定设置p在-Laplace操作者d -尺寸为的总和d单调强制运算符，每个都定义在不同的空间上。受这个例子的启发，当出现在有界变化项中的算子是具有不同解析和增长特性的算子的总和时，我们证明了由 Lévy 噪声驱动的一大类随机偏微分方程 (SPDE) 的存在性和唯一性结果。此外，允许算子局部单调，而不会明确限制出现在随机积分中的算子的增长。这是通过确定适当的矫顽力条件来完成的。因此，Lévy 的适定性驱动随机各向异性p- 拉普拉斯方程已显示。迄今为止，我们的框架是最通用的。许多流行的 SPDE 出现在现实世界模型中，例如随机 Ginzburg-Landau 方程和随机 Swift-Hohenberg 方程，两者都由 Lévy 噪声驱动，适合我们的设置。这些方程没有包含在文献中的相应结果中。