Existence and uniqueness are established for a degenerate second-order mean field game system in Hilbert spaces using viscosity solutions, adjoint equations, and an adapted Lasry-Lions monotonicity argument.
Villani,Optimal transport, Old and new, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 338, Springer-Verlag, Berlin
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Mean Field Games in Hilbert Spaces with Degenerate Diffusion: A Viscosity Solution Approach
Existence and uniqueness are established for a degenerate second-order mean field game system in Hilbert spaces using viscosity solutions, adjoint equations, and an adapted Lasry-Lions monotonicity argument.