Skip to main content
placeholder image

On Pogorelov estimates for Monge-Ampere type equations

Journal Article


Download full-text (Open Access)

Abstract


  • In this paper, we prove interior second derivative estimates of Pogorelov type for a general form of Monge-Ampère equation which includes the optimal transportation equation. The estimate extends that in a previous work with Xu-Jia Wang and assumes only that the matrix function in the equation is regular with respect to the gradient variables, that is it satisfies a weak form of the condition introduced previously by Ma,Trudinger and Wang for regularity of optimal transport mappings. We also indicate briefly an application to optimal transportation.

Authors


Publication Date


  • 2010

Citation


  • Liu, J. & Trudinger, N. S. (2010). On Pogorelov estimates for Monge-Ampere type equations. Discrete and Continuous Dynamical Systems Series A, 28 (3), 1121-1135.

Scopus Eid


  • 2-s2.0-77955326794

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1623&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/617

Number Of Pages


  • 14

Start Page


  • 1121

End Page


  • 1135

Volume


  • 28

Issue


  • 3

Abstract


  • In this paper, we prove interior second derivative estimates of Pogorelov type for a general form of Monge-Ampère equation which includes the optimal transportation equation. The estimate extends that in a previous work with Xu-Jia Wang and assumes only that the matrix function in the equation is regular with respect to the gradient variables, that is it satisfies a weak form of the condition introduced previously by Ma,Trudinger and Wang for regularity of optimal transport mappings. We also indicate briefly an application to optimal transportation.

Authors


Publication Date


  • 2010

Citation


  • Liu, J. & Trudinger, N. S. (2010). On Pogorelov estimates for Monge-Ampere type equations. Discrete and Continuous Dynamical Systems Series A, 28 (3), 1121-1135.

Scopus Eid


  • 2-s2.0-77955326794

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1623&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/617

Number Of Pages


  • 14

Start Page


  • 1121

End Page


  • 1135

Volume


  • 28

Issue


  • 3