Optimal controls of mean-field continuity equations are shown to be intrinsically Lipschitz in space when the control cost is sufficiently strongly convex, via uniform coercivity in Wasserstein calculus.
Global well-posedness of Master equations for deterministic displacement convex potential mean field games
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abstract
This manuscript constructs global in time solutions to the $master\ equations$ for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are $displacement\ convex$ and so, it may be in dichotomy with the class of so--called $monotone$ functions, widely considered in the literature. We construct solutions to both the scalar and vectorial master equations in potential Mean Field Games, when the underlying space is the whole space $\mathbb{R}^d$ and so, it is not compact.
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math.OC 1years
2019 1verdicts
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Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls
Optimal controls of mean-field continuity equations are shown to be intrinsically Lipschitz in space when the control cost is sufficiently strongly convex, via uniform coercivity in Wasserstein calculus.