The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

被引：1
|
作者：
de Lira, Jorge H. S. [1 ]
Cruz, Flavio F. [2 ]
机构：
[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil
[2] Univ Reg Cariri, Dept Matemat, BR-63041141 Juazeiro Do Norte, Ceara, Brazil
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2013年 / 62卷 / 03期
关键词：
Fully nonlinear elliptic PDEs; curvature equations; CONSTANT MEAN-CURVATURE; LOCALLY CONVEX HYPERSURFACES; NONLINEAR ELLIPTIC-EQUATIONS; PRESCRIBED GAUSS CURVATURE; BOUNDARY-VALUE-PROBLEMS; MONGE-AMPERE EQUATIONS; HESSIAN EQUATIONS; X R; GRAPHS; EXISTENCE;
D O I：
10.1512/iumj.2013.62.4996
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allow us to extend some of the existence theorems of Caffarelli, Nirenberg, and Spruck [4], and Ivochkina, Trudinger, and Lin [18], [19], [25] to more general curvature functions under mild conditions on the geometry of the domain.
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页码：815 / 854
页数：40
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