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arXiv · 1009.1834

The first boundary value problem for Abreu's equation

Bin Zhou
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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.

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Bin Zhou. 2010-09-09. The first boundary value problem for Abreu's equation. https://arxiv.org/abs/1009.1834

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