A microscopic convexity principle for nonlinear partial differential equations

被引：77

作者：

Bian, Baojun ^{[2
]}

Guan, Pengfei ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

INVENTIONES MATHEMATICAE | 2009年 / 177卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

BOUNDARY-VALUE-PROBLEMS; ELLIPTIC-EQUATIONS; WEINGARTEN CURVATURE; MEAN-CURVATURE; MINKOWSKI; HYPERSURFACES; SURFACES; FLOW;

D O I：

10.1007/s00222-009-0179-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study microscopic convexity property of fully nonlinear elliptic and parabolic partial differential equations. Under certain general structure condition, we establish that the rank of Hessian a double dagger (2) u is of constant rank for any convex solution u of equation F(a double dagger (2) u,a double dagger u,u,x)=0. The similar result is also proved for parabolic equations. Some of geometric applications are also discussed.

引用

页码：307 / 335

页数：29

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