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Global regularity for the Monge-Ampère equation with natural boundary condition

Journal Article


Abstract


  • In this paper, we establish the global $C^{2,\alpha}$ and $W^{2,p}$

    regularity for the Monge-Amp\`ere equation $\det\,D^2u = f$ subject to boundary

    condition $Du(\Omega) = \Omega^*$, where $\Omega$ and $\Omega^*$ are bounded

    convex domains in the Euclidean space $\mathbb{R}^n$ with $C^{1,1}$ boundaries,

    and $f$ is a H\"older continuous function. This boundary value problem arises

    naturally in optimal transportation and many other applications.

Publication Date


  • 2018

Web Of Science Accession Number


Abstract


  • In this paper, we establish the global $C^{2,\alpha}$ and $W^{2,p}$

    regularity for the Monge-Amp\`ere equation $\det\,D^2u = f$ subject to boundary

    condition $Du(\Omega) = \Omega^*$, where $\Omega$ and $\Omega^*$ are bounded

    convex domains in the Euclidean space $\mathbb{R}^n$ with $C^{1,1}$ boundaries,

    and $f$ is a H\"older continuous function. This boundary value problem arises

    naturally in optimal transportation and many other applications.

Publication Date


  • 2018

Web Of Science Accession Number