Stochastic optimal control of a evolutionary $p$-Laplace equation with multiplicative Lévy noise

Abstract

In this article, we are interested in an initial value optimal control problem for a evolutionary $p$-Laplace equation driven by multiplicative Lévy noise. We first present wellposedness of a weak solution by using an implicit time discretization of the problem, along with the Jakubowski version of the Skorokhod theorem for a non-metric space. We then formulate associated control problem, and establish existence of an optimal solution by using variational method and exploiting the convexity property of the cost functional.

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• Global L_2-solutions of stochastic Navier-Stokes equations
• Stochastic Reaction-diffusion Equations Driven by Jump Processes