论文标题
分数Malmheden定理
The Fractional Malmheden Theorem
论文作者
论文摘要
我们提供了Schwarz和Malmheden关于谐波功能的经典结果的部分。由此，我们获得了$ s $ harmonic函数的表示公式，作为加权经典谐波函数的线性叠加，还需要一个新的证明分数harnack不平等。该证明还导致球中分数不平等的最佳常数。
We provide a fractional counterpart of the classical results by Schwarz and Malmheden on harmonic functions. From that we obtain a representation formula for $s$-harmonic functions as a linear superposition of weighted classical harmonic functions which also entails a new proof of the fractional Harnack inequality. This proof also leads to optimal constants for the fractional Harnack inequality in the ball.
