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Harmonic extension from the exterior of a cylinder
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-13 , DOI: 10.1090/proc/15172 Stephen J. Gardiner , Hermann Render
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-13 , DOI: 10.1090/proc/15172 Stephen J. Gardiner , Hermann Render
Abstract:Let 
be a harmonic function on an annular cylinder. It was recently shown that, if 
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 
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.
中文翻译：
圆柱体外部的谐波延伸
摘要：让一个圆环圆柱上的谐波函数。最近显示，如果消失在外圆柱边界分量上，则它对由径向反射形成的更大的环形圆柱具有谐波延伸。本文表明，如果在内部边界分量上消失，则持有另一种扩展结果。推论表明，在边界上消失的无限圆柱体外部的任何谐波函数都具有与圆柱体轴的补码的谐波扩展。
更新日期：2021-02-08
be a harmonic function on an annular cylinder. It was recently shown that, if 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 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. 中文翻译：
圆柱体外部的谐波延伸
摘要：让
一个圆环圆柱上的谐波函数。最近显示，如果消失在外圆柱边界分量上，则它对由径向反射形成的更大的环形圆柱具有谐波延伸。本文表明，如果在内部边界分量上消失，则持有另一种扩展结果。推论表明，在边界上消失的无限圆柱体外部的任何谐波函数都具有与圆柱体轴的补码的谐波扩展。
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