Systems of Fully Nonlinear Degenerate Elliptic Obstacle problems with Dirichlet boundary conditions

TL;DR

This paper establishes existence and uniqueness of viscosity solutions for fully nonlinear elliptic obstacle systems with interconnected obstacles, relevant to optimal switching problems.

Contribution

It introduces a novel framework for solving interconnected obstacle problems involving fully nonlinear operators, expanding the theoretical understanding of such systems.

Findings

Proved existence of viscosity solutions

Established uniqueness of solutions

Applied results to optimal switching problems

Abstract

In this paper we prove existence and uniqueness of viscosity solutions of elliptic systems associated to fully nonlinear operators for minimization problems that involve interconnected obstacles. This system appears, among other, in the theory of the so-called optimal switching problems on bounded domains.