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On the representation of harmonic functions by their values on lattice points

✍ Scribed by Kenneth F Andersen

Book ID
107800381
Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
155 KB
Volume
49
Category
Article
ISSN
0022-247X

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πŸ“œ SIMILAR VOLUMES

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In this work we study the behaviour of ∞-harmonic functions near isolated exceptional points. We discuss two situations: (i) when points are in the interior and (ii) when points are on a at portion of the boundary, on which a solution vanishes. We consider both bounded and unbounded solutions. Under

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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