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arXiv · 2203.06923

The Fractional Malmheden Theorem

Serena Dipierro·Giovanni Giacomin·Enrico Valdinoci
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Abstract

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.

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Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci. 2022-03-14. The Fractional Malmheden Theorem. https://arxiv.org/abs/2203.06923

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