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July  2010, 28(3): 1151-1164. doi: 10.3934/dcds.2010.28.1151

Principal curvature estimates for the convex level sets of semilinear elliptic equations

Sun-Yung Alice Chang 1, , Xi-Nan Ma 2, and  Paul Yang 1,

1. 

Department of Mathematics, Princeton University, Princeton NJ 08544, United States, United States
2. 

Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province, China

Received  March 2010 Revised  April 2010 Published  April 2010

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.
Keywords: semilinear elliptic equation., Curvature estimate, level sets.
Mathematics Subject Classification: 35J05, 53J6.
Citation: Sun-Yung Alice Chang, Xi-Nan Ma, Paul Yang. Principal curvature estimates for the convex level sets of semilinear elliptic equations. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 1151-1164. doi: 10.3934/dcds.2010.28.1151
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