An interior gradient estimate for the mean curvature equation of Killing graphs and applications

被引：0

作者：

M. Dajczer

J. H. de Lira

J. Ripoll

机构：

[1] Estrada Dona Castorina,IMPA

[2] Universidade Federal Do Ceara,Departamento De Matematica

[3] Universidade Federal Do Rio Grande Do Sul,Departamento De Matematica

来源：

Journal d'Analyse Mathématique | 2016年 / 129卷

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D O I：

暂无

中图分类号：

学科分类号：

摘要：

We extend the interior gradient estimate due to Korevaar-Simon for solutions of the mean curvature equation from the case of euclidean graphs to the general case of Killing graphs. Our main application is the proof of existence of Killing graphs with prescribed mean curvature function for continuous boundary data, thus extending a result due to Dajczer, Hinojosa, and Lira. In addition, we prove the existence and uniqueness of radial graphs in hyperbolic space with prescribed mean curvature function and asymptotic boundary data at infinity.

引用

页码：91 / 103

页数：12

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