HARMONIC EXTENSION FROM THE EXTERIOR OF A CYLINDER

摘要

Let h be a harmonic function on an annular cylinder. It was recently shown that, if h vanishes on the outer cylindrical boundary component, then it has a harmonic extension to a larger annular cylinder formed by radial reflection. This paper shows that a different kind of extension result holds if h instead vanishes on the inner boundary component. As a corollary it is shown that any harmonic function on the exterior of an infinite cylinder which vanishes on the boundary has a harmonic extension to the complement of the axis of the cylinder.