Principal curvature estimates for the convex level sets of semilinear
Sun-Yung Alice Chang - Department of Mathematics, Princeton University, Princeton NJ 08544, United States (email)
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.
Keywords: Curvature estimate, level sets, semilinear elliptic equation.
Received: March 2010; Revised: April 2010; Published: April 2010.
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