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June  2010, 28(2): 789-807. doi: 10.3934/dcds.2010.28.789

A structural condition for microscopic convexity principle

Baojun Bian 1, and  Pengfei Guan 2,

1. 

Department of mathematics, Tongji University, Shanghai 200092, China
2. 

Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6, Canada

Received  February 2010 Revised  April 2010 Published  April 2010

The arguments in paper [2] have been refined to prove a microscopic convexity principle for fully nonlinear elliptic equation under a more natural structure condition. We also consider the corresponding result for the partial convexity case.
Keywords: Convexity, partial convexity, constant rank principle., fully nonlinear equations.
Mathematics Subject Classification: Primary: 35K10, 35B9.
Citation: Baojun Bian, Pengfei Guan. A structural condition for microscopic convexity principle. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 789-807. doi: 10.3934/dcds.2010.28.789
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