Global second derivative estimates for the second boundary value problem of the prescribed affine mean curvature and Abreu's equations

Details Global second derivative estimates for the second boundary value problem of the prescribed affine mean curvature and Abreu's equations Global second derivative estimates for the second boundary value problem of the prescribed affine mean curvature and Abreu's equations

2012-02-10

arxiv.org/abs/1202.2191v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we prove the global second derivative estimates for the second
boundary value problem of the prescribed affine mean curvature equation where
the affine mean curvature is only assumed to be in $L^{p}$. Our result extends
previous result by Trudinger and Wang in the case of globally bounded affine
mean curvature and also covers Abreu's equation.

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