【摘要】 写这篇文章的目的,就是推导出三分谢尔宾斯基垫片(SG3)上的标准拉普拉斯算子。第一部分介绍了三分谢尔宾斯基垫片(分形集)。第二部分依据文献[2]的理论,首先定义了V0上的拉普拉斯算子D,D∈LA(V0);又在{Vm}m≥0构建了一个自相似拉普拉斯算子序列Hm;然后又给出了调和结构的定义,求出了三分谢尔宾斯基垫片的调和结构。最后依据了文献[4]的理论,采用了由简到繁的方法,推算出了SG3上的逐点标准拉普拉斯算子,它是SG3上图拉普拉斯算子的极限。更多还原

【Abstract】 In this paper,our purpose is to deduce the standard Laplacians on the SG3. In the first section,we introduced the level-3 Sierpinski gasket. In the second section,according to the theory of the reference[2],we defined initial D∈LA( V0) and constructed a sequence of self-similar Laplacians Hmon { Vm}m≥0and gave the definition of the harmonic structure in second section. Finally,according to the theory of the reference[4],we used the methods of from simplicity to complication and deduce a pointwise definition for the standard Laplacians on the SG3,which is the limit of the Laplacians on the graph approximations to SG3.更多还原