Principal curvature estimates for the convex level sets of semilinear elliptic equations
Sun-Yung Alice Chang Xi-Nan Ma Paul Yang
Discrete & Continuous Dynamical Systems - A 2010, 28(3): 1151-1164 doi: 10.3934/dcds.2010.28.1151
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

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