Skip to main content
placeholder image

Regularity of free boundaries in optimal transportation

Journal Article


Abstract


  • In this paper, we obtain some regularities of the free boundary in optimal

    transportation with the quadratic cost. Our first result is about the

    $C^{1,\alpha}$ regularity of the free boundary for optimal partial transport

    between convex domains for densities $f, g$ bounded from below and above. When

    $f, g \in C^\alpha$, and $\partial\Omega, \partial\Omega^*\in C^{1,1}$ are far

    apart, by adopting our recent results on boundary regularity of Monge-Amp\`ere

    equations \cite{CLW1}, our second result shows that the free boundaries are

    $C^{2,\alpha}$. As an application, in the last we also obtain these

    regularities of the free boundary in an optimal transport problem with two

    separate targets.

Publication Date


  • 2019

Citation


  • Chen, S., & Liu, J. (2019). Regularity of free boundaries in optimal transportation. Retrieved from http://arxiv.org/abs/1911.10790v2

Web Of Science Accession Number


Abstract


  • In this paper, we obtain some regularities of the free boundary in optimal

    transportation with the quadratic cost. Our first result is about the

    $C^{1,\alpha}$ regularity of the free boundary for optimal partial transport

    between convex domains for densities $f, g$ bounded from below and above. When

    $f, g \in C^\alpha$, and $\partial\Omega, \partial\Omega^*\in C^{1,1}$ are far

    apart, by adopting our recent results on boundary regularity of Monge-Amp\`ere

    equations \cite{CLW1}, our second result shows that the free boundaries are

    $C^{2,\alpha}$. As an application, in the last we also obtain these

    regularities of the free boundary in an optimal transport problem with two

    separate targets.

Publication Date


  • 2019

Citation


  • Chen, S., & Liu, J. (2019). Regularity of free boundaries in optimal transportation. Retrieved from http://arxiv.org/abs/1911.10790v2

Web Of Science Accession Number