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On regular and singular harmonic functions of three variables

✍ Scribed by Erwin Kreyszig


Publisher
Springer
Year
1959
Tongue
English
Weight
829 KB
Volume
4
Category
Article
ISSN
0003-9527

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πŸ“œ SIMILAR VOLUMES


On the Regularity of Harmonic Functions
✍ 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