Asymptotic mean value properties for fractional anisotropic operators
Claudia Bucur, Marco Squassina
TL;DR
This paper derives an asymptotic representation for harmonic functions related to anisotropic nonlocal operators and establishes a Bourgain-Brezis-Mironescu type limit formula for anisotropic nonlocal norms.
Contribution
It introduces new asymptotic formulas for anisotropic nonlocal operators and extends limit formulas to anisotropic nonlocal norms, advancing understanding of anisotropic fractional operators.
Findings
Asymptotic representation formula for anisotropic harmonic functions
Bourgain-Brezis-Mironescu type limit formula for anisotropic nonlocal norms
Extension of nonlocal operator analysis to anisotropic settings
Abstract
We obtain an asymptotic representation formula for harmonic functions with respect to a linear anisotropic nonlocal operator. Furthermore we get a Bourgain-Brezis-Mironescu type limit formula for a related class of anisotropic nonlocal norms.
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