Removable Singularities of Separately Harmonic Functions

Removable Singularities of Separately Harmonic Functions

Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D \ S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projecti...

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Veröffentlicht in:Journal of Siberian Federal University. Mathematics & Physics 2021-01, Vol.14 (3), p.369-375
Hauptverfasser: Imomkulov, Sevdiyor A., Abdikadirov, Sultanbay M.
Format: Artikel
Sprache:eng
Schlagworte:
Domains
Harmonic functions
Singularities
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Zusammenfassung:Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D \ S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.
ISSN:1997-1397
2313-6022
DOI:10.17516/1997-1397-2021-14-3-369-375