The fractional Malmheden theorem

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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.

Original languageEnglish
JournalMathematics In Engineering
Issue number2
Early online date14 Apr 2022
Publication statusPublished - 2023


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