Principal curvature estimates for the convex  level sets of semilinearelliptic equations

Sun-Yung Alice Chang; Xi-Nan Ma; Paul Yang

doi:10.3934/dcds.2010.28.1151

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2010, Volume 28, Issue 3: 1151-1164. Doi: 10.3934/dcds.2010.28.1151

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

1.
Department of Mathematics, Princeton University, Princeton NJ 08544
2.
Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province

Received: February 28, 2010

Revised: March 31, 2010

Published: August 2010

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Abstract

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.

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Mathematics Subject Classification: 35J05, 53J67.

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