Abstract
For a function continuous on a compact set X ⊂ ℝ3 and harmonic inside X, we obtain a criterion of uniform approximability by functions harmonic in a neighborhood of X in terms of the classical harmonic capacity. The proof is based on an improved localization scheme of A.G. Vitushkin, on a special geometric construction, and on the methods of the theory of singular integrals.
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Original Russian Text © M.Ya. Mazalov, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 279, pp. 120–165.
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Mazalov, M.Y. Criterion of uniform approximability by harmonic functions on compact sets in ℝ3 . Proc. Steklov Inst. Math. 279, 110–154 (2012). https://doi.org/10.1134/S008154381208010X
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DOI: https://doi.org/10.1134/S008154381208010X