The Fractional Malmheden Theorem
Analysis of PDEs
2022-03-15 v1
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 -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.
Cite
@article{arxiv.2203.06923,
title = {The Fractional Malmheden Theorem},
author = {Serena Dipierro and Giovanni Giacomin and Enrico Valdinoci},
journal= {arXiv preprint arXiv:2203.06923},
year = {2022}
}
Comments
Mathematics in Engineering, in press