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

Research output: Contribution to journalArticle

14 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1151-1164
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume28
Issue number3
DOIs
StatePublished - Nov 1 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Curvature estimate
  • Level sets
  • Semilinear elliptic equation

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