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1 June 2004 Interior curvature bounds for a class of curvature equations
Weimin Sheng, John Urbas, Xu-Jia Wang
Duke Math. J. 123(2): 235-264 (1 June 2004). DOI: 10.1215/S0012-7094-04-12321-8

Abstract

We derive interior curvature bounds for admissible solutions of a class of curvature equations subject to affine Dirichlet data, generalizing a well-known estimate of Pogorelov for equations of Monge-Ampère type. For equations for which convexity of the solution is the natural ellipticity assumption, the curvature bound is proved for solutions with C1,1 Dirichlet data. We also use the curvature bounds to improve and extend various existence results for the Dirichlet and Plateau problems.

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Weimin Sheng. John Urbas. Xu-Jia Wang. "Interior curvature bounds for a class of curvature equations." Duke Math. J. 123 (2) 235 - 264, 1 June 2004. https://doi.org/10.1215/S0012-7094-04-12321-8

Information

Published: 1 June 2004
First available in Project Euclid: 11 June 2004

zbMATH: 1174.35378
MathSciNet: MR2066938
Digital Object Identifier: 10.1215/S0012-7094-04-12321-8

Subjects:
Primary: 35J60
Secondary: 35B45 , 35D10 , 35J65 , 53C42

Rights: Copyright © 2004 Duke University Press

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Vol.123 • No. 2 • 1 June 2004
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