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On the second boundary value problem for Monge-Ampere type equations and optimal transportation

Authors
  • Trudinger, Neil S
  • Wang, Xu-jia
Type
Preprint
Publication Date
May 31, 2007
Submission Date
Jan 04, 2006
Identifiers
arXiv ID: math/0601086
Source
arXiv
License
Unknown
External links

Abstract

This paper is concerned with the existence of globally smooth solutions for the second boundary value problem for Monge-Ampere equations and the application to regularity of potentials in optimal transportation. The cost functions satisfy a weak form of our condition A3, under which we proved interior regularity in a recent paper with Xi-nan Ma. Consequently they include the quadratic cost function case of Caffarelli and Urbas as well as the various examples in the earlier work. The approach is through the derivation of global estimates for second derivatives of solutions.

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