Abstract
In this paper, we prove interior second derivative estimates of Pogorelov type for a general form of Monge-Ampere 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.
Highlights
There has been considerable research activity in recent years devoted to fully nonlinear, elliptic second order partial differential equations of the form [13],F [u] := F {D2u − A(·, Du)} = B(·, u, Du), (1)in domains Ω in Euclidean n-space, Rn, as well as their extensions to Riemannian manifolds
We prove interior second derivative estimates of Pogorelov type for a general form of Monge-Ampere 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
Summary
Follow this and additional works at: https://ro.uow.edu.au/eispapers Part of the Engineering Commons, and the Science and Technology Studies Commons. Recommended Citation Liu, Jiakun and Trudinger, Neil, "On Pogorelov estimates for Monge-Ampere type equations" (2010). Faculty of Engineering and Information Sciences - Papers: Part A. Faculty of Engineering and Information Sciences - Papers: Part A. 617. https://ro.uow.edu.au/eispapers/617
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
