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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the regularity of the complex Monge-Ampère equations

Author: Weiyong He
Journal: Proc. Amer. Math. Soc. 140 (2012), 1719-1727
MSC (2010): Primary 35J60, 35J96
Posted: September 9, 2011
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Abstract: We shall consider the regularity of solutions for the complex Monge-Ampère equations in $\mathbb{C}^n$ or a bounded domain. First we prove interior estimates of solutions in a bounded domain for the complex Monge-Ampère equations with the assumption of an bound for $\triangle u$ , , and of a Lipschitz condition on the right-hand side. Then we shall construct a family of Pogorelov-type examples for the complex Monge-Ampère equations. These examples give generalized entire solutions (as well as viscosity solutions) of the complex Monge-Ampère equation $\det(u_{i\bar j})=1$ in $\mathbb{C}^n$ .

References

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