PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS

被引：23

作者：

Chang, Sun-Yung Alice ^{[1
]}

Ma, Xi-Nan ^{[2
]}

Yang, Paul ^{[3
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[3] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 03期

基金：

美国国家科学基金会;

关键词：

Curvature estimate; level sets; semilinear elliptic equation; PARALLEL PLANES; CURVES; SURFACES; RINGS;

D O I：

10.3934/dcds.2010.28.1151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary gradient. We also extend this result to a class of semi-linear elliptic partial differential equations under certain structure condition.

引用

页码：1151 / 1164

页数：14

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