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Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case
In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently established by De Philippis and Figalli [14 De Philippis , G. , Figalli , A. W2, 1 regularity for solutions of the Monge-Ampère equation. Preprint. [Google Scholar]], to provide global in time existence …