Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 27, pp. 1-18.

Title: Existence of solutions to stochastic p(t,x)-Laplace equations and applications

Authors: Chen Liang (Harbin Institute of Tech., Harbin, Heilongjiang, China)
         Lixu Yan (Northeast Forestry Univ., Harbin, Heilongjiang, China)
         Yongqiang Fu (Harbin Institute of Tech., Harbin, Heilongjiang, China)

Abstract:
In this article, we consider a stochastic $p(t,x)$-Laplace equation. First
we use the Galerkin method toobtain a unique weak solution.
Then we obtain optimal controls for the corresponding stochastic optimal control problem

Submitted October 7, 2023. Published March 27, 2024.
Math Subject Classifications: 35K92, 60H15.
Key Words: Stochastic p(t,x)-Laplace equation; weak solution; optimal control; Galerkin method.