# Stochastic optimal control of a evolutionary $p$-Laplace equation with multiplicative L\'{e}vy noise

## TL;DR

This paper studies the optimal control of a stochastic p-Laplace equation influenced by multiplicative Lévy noise, establishing well-posedness and existence of optimal solutions using variational methods.

## Contribution

It introduces a novel approach to control stochastic p-Laplace equations with Lévy noise, proving well-posedness and optimal control existence under new conditions.

## Key findings

- Well-posedness of weak solutions established
- Existence of optimal control proven
- Use of Skorokhod theorem in non-metric spaces

## Abstract

In this article, we are interested in an initial value optimal control problem for a evolutionary $p$-Laplace equation driven by multiplicative L\'{e}vy 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.