Regularity of Monge-Ampere type equations arising in optimal transportation
In this thesis we study the regularity problem in optimal transportation, by establishing the a priori estimates for a class of Monge-Ampere type equations. This thesis consists of four chapters. Chapter 1 is an introduction. In Chapter 2 we study Monge's mass transfer problem. Chapter 3 concerns the regularity of optimal transportation on manifolds. In the last Chapter we deal with the homogeneous Monge-Ampere equations. The regularity is a main issue in optimal transportation, and has...[Show more]
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