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

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

2006-01-05

arxiv.org/abs/math/0601086v4

Mathematics

Analysis of PDEs

In this version, we remove a hypothesis,used previously for the continuity method, through direct construction of a uniformly

Scientific paper

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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