On the regularity of the complex Monge-Ampère equations
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- by Weiyong He PDF
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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 $C^2$ estimates of solutions in a bounded domain for the complex Monge-Ampère equations with the assumption of an $L^p$ bound for $\triangle u$, $p>n^2$, 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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Additional Information
- Weiyong He
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
- MR Author ID: 812224
- Email: whe@uoregon.edu
- Received by editor(s): June 7, 2010
- Received by editor(s) in revised form: January 25, 2011
- Published electronically: September 9, 2011
- Additional Notes: The author is partially supported by an NSF grant.
- Communicated by: Chuu-Lian Terng
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1719-1727
- MSC (2010): Primary 35J60, 35J96
- DOI: https://doi.org/10.1090/S0002-9939-2011-11178-X
- MathSciNet review: 2869156