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.
Asymptotic mean value properties for fractional anisotropic operators / C. Bucur, M. Squassina. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 466:1(2018), pp. 107-126. [10.1016/j.jmaa.2018.05.063]
Asymptotic mean value properties for fractional anisotropic operators
C. BucurPrimo
;
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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