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arXiv:1811.12531 [math.AP]AbstractReferencesReviewsResources

Global $W^{2,1+\varepsilon}$ estimates for Monge-Ampère equation with natural boundary condition

Ovidiu Savin, Hui Yu

Published 2018-11-29Version 1

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.

Comments: 13 pages
Categories: math.AP
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