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Harmonic Shears of Regular Polygons by Hypergeometric Functions

✍ Scribed by Kathy Driver; Peter Duren

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
985 KB
Volume
239
Category
Article
ISSN
0022-247X

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πŸ“œ SIMILAR VOLUMES

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## Abstract We prove that bounded harmonic functions of anisotropic fractional Laplacians are HΓΆlder continuous under mild regularity assumptions on the corresponding LΓ©vy measure. Under some stronger assumptions the Green function, Poisson kernel and the harmonic functions are even differentiable

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A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d Ξ΄ = Ξ΄Z d βŠ‚ R d with spacing Ξ΄ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-HΓΆlder continuous, Ξ΄ β†’ 0. These results are then applied to establish regularity