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arXiv cs/02090202002-09-18math.NAcs.CEcs.NA

分数阶拉普拉斯算子的一个新定义

A new definition of the fractional Laplacian

W. Chen

备注：: This study is carred out with the ongoing project of "mathematical and numerical modelling of medical ultasound wave propagation" sponsored by the Simula Research Laboratory

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AI总结：

针对分数阶拉普拉斯算子标准定义中的超奇异积分与边界条件实施难题，提出新定义以克服这些缺陷。

摘要：

注意到分数阶拉普拉斯算子的标准定义会导致超奇异卷积积分，并且在如何实施边界条件方面也不明确。本注释的目的是引入分数阶拉普拉斯算子的一个新定义，以克服这些主要缺陷。

英文摘要：

It is noted that the standard definition of the fractional Laplacian leads to a hyper-singular convolution integral and is also obscure about how to implement the boundary conditions. This purpose of this note is to introduce a new definition of the fractional Laplacian to overcome these major drawbacks.

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