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A uniqueness result for harmonic functions

Authors:	Richard F Bass

Institution:	Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Abstract:	Let $d\geq 2$ , $D=\mathbb{R}^{d}\times (0,\infty )$ , and suppose is harmonic in and $C^{2}$ on the closure of . If the gradient of vanishes continuously on a subset of $\partial D$ of positive -dimensional Lebesgue measure and satisfies certain regularity conditions, then must be identically constant.

Keywords:	Harmonic Privalov unique continuation diffusions Bessel processes

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