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

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."