A Priori Estimates for Monge-Ampere Equation and Applications
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In this thesis we study different applications of the Monge-Ampere type equations. Chapter 1 is an introduction. In Chapter 2, we study the convergence rate of discrete Monge-Ampere type equation. In Chapter 3 we study the Lp-dual Minkowski problem. In Chapter 4 we study the asymptotic affine hyperspheres. The numerical solution to Monge-Ampere equation, in particular the Dirichlet problem has drawn much attentions in last 20 years. Different algorithms have been designed to simulate...[Show more]
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