边值问题虚拟压缩恢复原理及其在Bjerhammar理论中的一个应用

The Fictitious Compress Recuperation Principle in Boundary Value Problems and Its Application in Bjerhammar's Theory

在引力位虚拟压缩恢复法的基础上,进一步发展该法,使其适合于任意一个正则调和函数u。对于任意一个有限单连通形体Ω(其边界是简单封闭曲面),假如给定了边值u|Ω,并且假定u在上述形体的外部调和,在无穷远处正则,则可根据虚拟压缩恢复思想精确而严密地求出整个外部空间的u场。于是,可将虚拟压缩恢复法提升为虚拟压缩恢复原理。作为一个应用实例,本文简明地给出了Bjerhammar理论所需要的虚拟重力异常。

The fictitious compress recuperation method is further developed, so that it is suitable for any regular harmonic function u. For an arbitrary finite body Ω with a simply closed surface, if the boundary value u|(Ω) was given, and it is assumed that the function u is harmonic in the region outside the body and regular at infinity, one can precisely and strictly determine the external field u by using the idea of the fictitious compress recuperation. Hence, it is reasonable to generalize the method of the fictitious compress recuperation into the corresponding principle. Furthermore, as an application example, the fictitious gravity anomaly required in Bjerhammar's theory is simply derived out, based on the principle of the fictitious compress recuperation.