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arXiv · 1811.12531

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

Ovidiu Savin·Hui Yu
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Abstract

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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Ovidiu Savin, Hui Yu. 2018-11-29. Global $W^{2,1+\varepsilon}$ estimates for Monge-Amp\`ere equation with natural boundary condition. https://arxiv.org/abs/1811.12531

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