  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.
