Global W^(2,1+varepsilon) estimates for Monge-Amp\`ere equation with natural boundary condition
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boundaryconditionequationmonge-ampnaturalvarepsilonarisingaway
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For the Monge-Amp\`ere equation with a right-hand side bounded away from 0 and infinity, we show that the solution, subject to the natural boundary condition arising in optimal transport, is in $W^{2,1+\varepsilon}$ up to the boundary.
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