Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations

Peihe Wang; Wei Zhang

doi:10.4208/jpde.v25.n3.4

Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations

Authors

Peihe Wang School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Wei Zhang Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia

DOI:

https://doi.org/10.4208/jpde.v25.n3.4

Keywords:

Gaussian curvature estimates;convex level sets;minimal surface;semilinear elliptic equation;maximum principle

Abstract

We give lower bound estimates for the Gaussian curvature of convex level sets of minimal surfaces and the solutions to semilinear elliptic equations in terms of the norm of boundary gradient and the Gaussian curvature of the boundary.

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Published

2012-09-02

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Issue

Vol. 25 No. 3 (2012)

Section

Articles

How to Cite

Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations. (2012). Journal of Partial Differential Equations, 25(3), 239-275. https://doi.org/10.4208/jpde.v25.n3.4