Weingarten hypersurfaces with prescribed gradient image

John Urbas

doi:10.1007/s002090100362

Weingarten hypersurfaces with prescribed gradient image

John Urbas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We prove the existence of globally smooth convex solutions u of a class of curvature equations subject to the boundary condition Du(Ω) = Ω* where Ω and Ω* are smooth uniformly convex domains in Rⁿ. The results generalize some of our previous work on the two dimensional case, and on Hessian equations in all dimensions.

Original language	English
Pages (from-to)	53-82
Number of pages	30
Journal	Mathematische Zeitschrift
Volume	240
Issue number	1
DOIs	https://doi.org/10.1007/s002090100362
Publication status	Published - May 2002

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10.1007/s002090100362

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title = "Weingarten hypersurfaces with prescribed gradient image",

abstract = "We prove the existence of globally smooth convex solutions u of a class of curvature equations subject to the boundary condition Du(Ω) = Ω* where Ω and Ω* are smooth uniformly convex domains in Rn. The results generalize some of our previous work on the two dimensional case, and on Hessian equations in all dimensions.",

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AB - We prove the existence of globally smooth convex solutions u of a class of curvature equations subject to the boundary condition Du(Ω) = Ω* where Ω and Ω* are smooth uniformly convex domains in Rn. The results generalize some of our previous work on the two dimensional case, and on Hessian equations in all dimensions.

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

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Weingarten hypersurfaces with prescribed gradient image

Abstract

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