\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2008, Volume 7, Issue 4: 853-865. Doi: 10.3934/cpaa.2008.7.853
This issue Previous Article Local existence and blowup criterion of the Lagrangian averaged Euler equations in Besov spaces Next Article Sharp well-posedness results for the Kuramoto-Velarde equation

Limits for Monge-Kantorovich mass transport problems

  • 1.

    Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid

  • 2.

    Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

  • 3.

    Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid

  • 4.

    IMDEA Matematicas, C-IX, Campus UAM, 28049 Madrid

Received:  August 31, 2006
Revised:  January 31, 2007
Published:  June 2008
Abstract Related Papers Cited by
    Abstract
  • In this paper we study the limit of Monge-Kantorovich mass transfer problems when the involved measures are supported in a small strip near the boundary of a bounded smooth domain, $\Omega$. Given two absolutely continuos measures (with respect to the surface measure) supported on the boundary $\partial \Omega$, by performing a suitable extension of the measures to a strip of width $\varepsilon$ near the boundary of the domain $\Omega$ we consider the mass transfer problem for the extensions. Then we study the limit as $\varepsilon$ goes to zero of the Kantorovich potentials for the extensions and obtain that it coincides with a solution of the original mass transfer problem. Moreover we look for the possible approximations of these problems by solutions to equations involving the $p-$Laplacian for large values of $p$.
    Mathematics Subject Classification: Primary: 35J65, 35J50, 35J55.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(95) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2023 American Institute of Mathematical Sciences