An elliptic partial differential equations system and its application

TL;DR

This paper investigates the existence of solutions for a novel elliptic PDE system using sub- and super-solutions, and applies it to a stochastic control problem, filling a gap in existing research.

Contribution

Introduces a new elliptic PDE system and demonstrates its application to stochastic control, employing the sub- and super-solutions method.

Findings

Established existence of solutions for the new system.

Applied the system to a stochastic control problem.

System not previously considered in literature.

Abstract

This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented. This system seemed not considered before.