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Holder regularity of optimal mappings in optimal transportation

Journal Article


Abstract


  • It is known that optimal mappings in optimal transportation problems are

    uniquely determined by corresponding potential functions. In this paper we prove various

    local properties of potential functions. In particular we obtain the C1,α regularity of potential

    functions with optimal exponent α, which improves previous regularity results of Loeper.

Publication Date


  • 2009

Citation


  • Liu, J. (2009). Holder regularity of optimal mappings in optimal transportation. Calculus of Variations and Partial Differential Equations, 34 (4), 435-451.

Scopus Eid


  • 2-s2.0-59449088789

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/614

Number Of Pages


  • 16

Start Page


  • 435

End Page


  • 451

Volume


  • 34

Issue


  • 4

Abstract


  • It is known that optimal mappings in optimal transportation problems are

    uniquely determined by corresponding potential functions. In this paper we prove various

    local properties of potential functions. In particular we obtain the C1,α regularity of potential

    functions with optimal exponent α, which improves previous regularity results of Loeper.

Publication Date


  • 2009

Citation


  • Liu, J. (2009). Holder regularity of optimal mappings in optimal transportation. Calculus of Variations and Partial Differential Equations, 34 (4), 435-451.

Scopus Eid


  • 2-s2.0-59449088789

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/614

Number Of Pages


  • 16

Start Page


  • 435

End Page


  • 451

Volume


  • 34

Issue


  • 4