@article{c68bfebab4fa4bc08d3334adb1a70d12,
title = "The fractional Malmheden theorem",
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.",
keywords = "fractional Laplacian, geometric properties of harmonic functions, Harnack inequality, Malmheden theorem, Poisson kernel, Schwarz theorem",
author = "Serena Dipierro and Giovanni Giacomin and Enrico Valdinoci",
note = "Funding Information: SD and EV are members of AustMS. Supported by the Australian Laureate Fellowship FL190100081 “Minimal surfaces, free boundaries and partial differential equations” and by the Australian Research Council DECRA DE180100957 “PDEs, free boundaries and applications”. Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press.",
year = "2023",
doi = "10.3934/mine.2023024",
language = "English",
volume = "5",
journal = "Mathematics In Engineering",
issn = "2640-3501",
publisher = "American Institute of Mathematical Sciences",
number = "2",
}