Malmheden定理的再认识
Malmheden's theorem revisited
摘要：
1934年H. Malmheden发现了一个优雅的几何算法解决狄利克雷问题在一个球。虽然他的结果在23年后被达芬独立地重新发现，但似乎仍然没有广为人知。在本文中，我们回到Malmheden定理，给出该结果的另一种证明，该结果允许推广到多调和函数，并且还讨论了他的定理在欧几里得空间中球的调和测度的几何性质中的应用。
英文摘要：
In 1934 H. Malmheden discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in Euclidean spaces.
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