2021/05/18 by Michele Ricciardi, Ricciardi, Michele · 2 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2105.08662
openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study the well-posedness of the Master Equation of Mean Field Games in a framework of Neumann boundary condition. The definition of solution is closely related to the classical one of the Mean Field Games system, but the boundary condition here leads to two Neumann conditions in the Master Equation formulation, for both space and measure. The global regularity of the linearized system, which is crucial in order to prove the existence of solutions, is obtained with a deep study of the boundary conditions and the global regularity at the boundary of a suitable class of parabolic equations.