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

Pages: 1151 - 1164, Volume 28, Issue 3, November 2010

doi:10.3934/dcds.2010.28.1151       Abstract        Full Text (183.5K)       Related Articles

Sun-Yung Alice Chang - Department of Mathematics, Princeton University, Princeton NJ 08544, United States (email)
Xi-Nan Ma - Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province, China (email)
Paul Yang - 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.
Mathematics Subject Classification:  35J05, 53J67.

Received: March 2010;      Revised: April 2010;      Published: April 2010.