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.
Bucur, C., Squassina, M. (2018). Asymptotic mean value properties for fractional anisotropic operators. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 466(1), 107-126 [10.1016/j.jmaa.2018.05.063].
Asymptotic mean value properties for fractional anisotropic operators
Bucur C.
;
2018
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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