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**Distributed Solutions to Complex Societal Problems Reunion Workshop**## Viscosity Solutions for McKean-Vlasov Control on a torus

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Mete Soner, Princeton University
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**Tuesday, February 21, 2023**

**Abstract**: We consider the viscosity solutions of the dynamic programming equations of a McKean Vlasov control defined using the intrinsic linear derivative. We obtain a comparison result between the Lipschitz viscosity sub and super solutions under a structural assumption on the control set together with the given functions. Proof follows the classical variable doubling argument of Crandall & Lions by using a novel smooth Fourier-Wasserstein metric that we construct. The value function is also shown to be Lipschitz continuous with respect to this metric. This is joint work with Qinxin Yan of Princeton University.