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Volume 28, Issue 3
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

J. Part. Diff. Eq., 28 (2015), pp. 197-207.

Published online: 2015-09

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  • 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.
  • Keywords

Harmonic function maximum principle level set

  • AMS Subject Headings

35B45, 35J92, 35B50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

kongs@ustc.edu.cn (Shengli Kong)

jjxujane@shu.edu.cn (Jinju Xu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-197, author = {Kong , Shengli and Xu , Jinju}, title = {A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {3}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/5110.html} }
TY - JOUR T1 - A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes AU - Kong , Shengli AU - Xu , Jinju JO - Journal of Partial Differential Equations VL - 3 SP - 197 EP - 207 PY - 2015 DA - 2015/09 SN - 28 DO - http://doi.org/10.4208/jpde.v28.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/5110.html KW - Harmonic function KW - maximum principle KW - level set AB - 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.
Kong , Shengli and Xu , Jinju. (2015). A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes. Journal of Partial Differential Equations. 28 (3). 197-207. doi:10.4208/jpde.v28.n3.1
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