A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes

Shengli Kong; Jinju Xu

doi:10.4208/jpde.v28.n3.1

A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes

Authors

Shengli Kong Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
Jinju Xu Department of Mathematics, Shanghai University, Shanghai 200444, China

DOI:

https://doi.org/10.4208/jpde.v28.n3.1

Keywords:

Harmonic function;maximum principle;level set

Abstract

" In this paper,we find two auxiliary functions andmake use of themaximum principle to study the level sets of harmonic function defined on a convex ring with homogeneous Dirichlet boundary conditions in $\\mathbb{R}^2$. In higher dimensions, we also have a similar result to Jagy's."

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Published

2015-09-05

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Issue

Vol. 28 No. 3 (2015)

Section

Articles

How to Cite

A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes. (2015). Journal of Partial Differential Equations, 28(3), 197-207. https://doi.org/10.4208/jpde.v28.n3.1