Global C2-Estimates for Convex Solutions of Curvature Equations

被引：72

作者：

Guan, Pengfei ^{[1
]}

Ren, Changyu ^{[2
]}

Wang, Zhizhang ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada

[2] Jilin Univ, Sch Math Sci, Changchun 130023, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2015年 / 68卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

2ND-ORDER ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM; MINKOWSKI PROBLEM; HESSIAN EQUATION; MEAN-CURVATURE; HYPERSURFACES; MANIFOLDS;

D O I：

10.1002/cpa.21528

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a C-2 a priori estimate for convex hypersurfaces whose principal curvatures kappa=(kappa(1),..., kappa(n)) satisfy sigma(k)((X))=f(X,(X)), the Weingarten curvature equation. We also obtain such an estimate for admissible 2-convex hypersurfaces in the case k=2. Our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations.(c) 2015 Wiley Periodicals, Inc.

引用

页码：1287 / 1325

页数：39

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