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Densities with the mean value property for harmonic functions in a Lipschitz domain

Authors:	Hiroaki Aikawa

Institution:	Department of Mathematics, Shimane University, Matsue 690, Japan

Abstract:	Let be a bounded domain in $\mathbb {R}^{n}$ , $n\ge 2$ , and let $x_{0}\in D$ . We consider positive functions on such that $h( x_{0}) = (\int _{D}w dx)^{-1} \int _{D} h w dx$ for all bounded harmonic functions on . We determine Lipschitz domains having such with $\inf _{D} w>0$ .

Keywords:	Harmonic functions mean value property gradient of harmonic function

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