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

Analysis of PDEs 2018-12-03 v1

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 W2,1+εW^{2,1+\varepsilon} up to the boundary.

Keywords

Cite

@article{arxiv.1811.12531,
  title  = {Global $W^{2,1+\varepsilon}$ estimates for Monge-Amp\`ere equation with natural boundary condition},
  author = {Ovidiu Savin and Hui Yu},
  journal= {arXiv preprint arXiv:1811.12531},
  year   = {2018}
}

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13 pages