Local Regularity of the Complex Monge-Ampere Equation

In this thesis, we present a self-contained account of the current development in the local regularity theory of the complex Monge-Ampere equation through the modern fully-nonlinear PDE point of view. We have apply the modern elliptic techniques to establish new local regularity results. These includes: regularity of small perturbed solutions, Holder regularity of the Hessian of the W^{2,p} solutions and a Liouville-type theorem.

Author dc:creator

• Wang, Yu

• Mathematics
• Monge-Ampère equations
• Differential equations, Partial

Language dc:language

English

DOI dc:identifier

https://doi.org/10.7916/D8NS124V

OAI identifier oai:identifier

oai:academiccommons.columbia.edu:10.7916/D8NS124V