The first boundary value problem for Abreu's equation
Analysis of PDEs
2010-09-10 v1
Abstract
In this paper we prove the existence and regularity of solutions to the first boundary value problem for Abreu's equation, which is a fourth order nonlinear partial differential equation closely related to the Monge-Ampere equation. The first boundary value problem can be formulated as a variational problem for the energy functional. The existence and uniqueness of maximizers can be obtained by the concavity of the functional. The main ingredients of the paper are the a priori estimates and an approximation result, which enable us to prove that the maximizer is smooth in dimension 2.
Cite
@article{arxiv.1009.1834,
title = {The first boundary value problem for Abreu's equation},
author = {Bin Zhou},
journal= {arXiv preprint arXiv:1009.1834},
year = {2010}
}