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

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