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Regularity Theory and Traces of A-Harmonic Functions

✍ Scribed by Pekka Koskela, Juan J. Manfredi and Enrique Villamor

Book ID
125700661
Publisher
American Mathematical Society
Year
1996
Tongue
English
Weight
809 KB
Volume
348
Category
Article
ISSN
0002-9947

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πŸ“œ SIMILAR VOLUMES

Regularity of harmonic functions for ani
Regularity of harmonic functions for anisotropic fractional Laplacians
✍ PaweΕ‚ Sztonyk πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 230 KB

## 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

On the Regularity of Harmonic Functions
On the Regularity of Harmonic Functions and Spherical Harmonic Maps Defined on Lattices
✍ Lawrence E. Thomas πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 140 KB

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