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

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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

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

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