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Interior C 2,alpha regularity for potential functions in optimal transportation

Journal Article


Abstract


  • In this paper we study the continuity of second derivatives of solutions to the

    Monge–Ampère equation arising in optimal transportation. We obtain Hölder and

    more general continuity estimates for second derivatives, when the inhomogeneous

    term is Hölder and Dini continuous, together with corresponding regularity results

    for potentials.

Authors


  •   Liu, Jiakun
  •   Trudinger, Neil (external author)
  •   Wang, Xu-Jia (external author)

Publication Date


  • 2009

Citation


  • Liu, J., Trudinger, N. S. & Wang, X. (2009). Interior C 2,alpha regularity for potential functions in optimal transportation. Communications in Partial Differential Equations, 35 (1), 165-184.

Scopus Eid


  • 2-s2.0-74949099148

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/616

Number Of Pages


  • 19

Start Page


  • 165

End Page


  • 184

Volume


  • 35

Issue


  • 1

Abstract


  • In this paper we study the continuity of second derivatives of solutions to the

    Monge–Ampère equation arising in optimal transportation. We obtain Hölder and

    more general continuity estimates for second derivatives, when the inhomogeneous

    term is Hölder and Dini continuous, together with corresponding regularity results

    for potentials.

Authors


  •   Liu, Jiakun
  •   Trudinger, Neil (external author)
  •   Wang, Xu-Jia (external author)

Publication Date


  • 2009

Citation


  • Liu, J., Trudinger, N. S. & Wang, X. (2009). Interior C 2,alpha regularity for potential functions in optimal transportation. Communications in Partial Differential Equations, 35 (1), 165-184.

Scopus Eid


  • 2-s2.0-74949099148

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/616

Number Of Pages


  • 19

Start Page


  • 165

End Page


  • 184

Volume


  • 35

Issue


  • 1