We consider the anisotropic version of an extension problem studied by Caffarelli and Silvestre. We present the anisotropic fractional Laplacian and prove the Almgren’s frequency formula obtained by Caffarelli and Silvestre for the anisotropic case.

中文翻译：

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与各向异性分数拉普拉斯算子有关的扩展问题的阿尔姆格伦频率公式

我们考虑了Caffarelli和Silvestre研究的扩展问题的各向异性版本。我们给出了各向异性分数阶拉普拉斯算子，并证明了Caffarelli和Silvestre在各向异性情况下获得的Almgren频率公式。