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Uniform Approximation on Closed Sets by Harmonic Functions with Newtonian Singularities
Author(s) -
Gauthier P. M.,
Goldstein M.,
Ow W. H.
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-28.1.71
Subject(s) - gravitational singularity , harmonic , harmonic function , mathematics , newtonian fluid , mathematical analysis , function (biology) , pure mathematics , physics , classical mechanics , acoustics , evolutionary biology , biology
Let F be a closed subset of R n , n > 2. We show that each function harmonic on F can be approximated uniformly by functions harmonic on R n except possibly for Newtonian singularities. Moreover, it is possible to approximate finitely many partial derivatives simultaneously.