The Master Equation in a Bounded Domain under Invariance Conditions for the State Space

2022/11/11 by Zitridis, Antonios · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.06514

Abstract

In this paper, we study the well-posedness (existence and uniqueness) of the Master Equation of Mean Field Games under invariance-type conditions, otherwise known as viability conditions for the controlled dynamics. The interior regularity of the solutions of the associated Mean Field Game system and its linearized version, which plays a crucial role in the proof of the existence, is obtained by the global regularity of the corresponding solutions in the Neumann boundary conditions case. Finally, we prove that the solution of the related Nash system converges to the solution of the Master Equation.

Cited by

• Mean Field Games of Controls with Boundary Conditions & Invariance Constraints

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• The Master Equation in a Bounded Domain with Neumann Conditions
• Mean field games under invariance conditions for the state space
• The Convergence Problem in Mean Field Games with Neumann Boundary Conditions
• Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data
• Mean Field Game Master Equations with Anti-monotonicity Conditions