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

Issue

Vol. 28 No. 3 (2015)

Section

Articles