  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.
