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

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

Year:    2015

Author:    Shengli Kong, Jinju Xu

Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 3 : pp. 197–207

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 3 : pp. 197–207

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Harmonic function

Author Details

Shengli Kong

Jinju Xu

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