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

Sun Yung Alice Chang; Xi Nan Ma; Paul Yang

doi:10.3934/dcds.2010.28.1151

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

Sun Yung Alice Chang, Xi Nan Ma, Paul Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

20 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 language	English (US)
Pages (from-to)	1151-1164
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems
Volume	28
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2010.28.1151
State	Published - Nov 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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10.3934/dcds.2010.28.1151

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title = "Principal curvature estimates for the convex level sets of semilinear elliptic equations",

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",

author = "Chang, {Sun Yung Alice} and Ma, {Xi Nan} and Paul Yang",

year = "2010",

month = nov,

doi = "10.3934/dcds.2010.28.1151",

language = "English (US)",

volume = "28",

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journal = "Discrete and Continuous Dynamical Systems",

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T1 - Principal curvature estimates for the convex level sets of semilinear elliptic equations

AU - Chang, Sun Yung Alice

AU - Ma, Xi Nan

AU - Yang, Paul

PY - 2010/11

Y1 - 2010/11

N2 - 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.

AB - 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.

KW - Curvature estimate

KW - Level sets

KW - Semilinear elliptic equation

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SN - 1078-0947

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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