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

Majee, Ananta K. 

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 100.

Résumé

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.

Détail

DOI : 10.1051/cocv/2020028

Classification : 45K05, 46S50, 49L20, 49L25, 91A23, 93E20
Keywords: Evolutionary $p$-Laplace equation, stochastic PDEs, weak solution, Skorokhod theorem

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