The Master Equation in a Bounded Domain with Absorption

TL;DR

This paper studies the Master Equation in Mean Field Games within a bounded domain with absorption, focusing on well-posedness and regularity of solutions for a class of parabolic equations.

Contribution

It establishes the well-posedness and regularity of the Master Equation in a bounded domain with absorption, extending MFG theory to new boundary conditions.

Findings

Proved well-posedness of the Master Equation with Dirichlet boundary conditions.

Analyzed regularity properties of solutions in the context of bounded domains.

Extended the theoretical framework of MFGs to include absorption at boundaries.

Abstract

We analyze the Master Equation within Mean Field Games (MFG) theory considering a bounded domain with homogeneous Dirichlet conditions. Concerning the N-players differential game, the player's dynamic ends when touching the boundary. We analyze the well-posedness of the Master Equation and the regularity of its solutions for a suitable class of parabolic equations.