On the Regularity of Harmonic Functions
β
Lawrence E. Thomas
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Article
π
2001
π
Elsevier Science
π
English
β 140 KB
A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d Ξ΄ = Ξ΄Z d β 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