Geodesic
A criterion for approximability by harmonic functions in Lipschitz spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 144-171

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Let $X$ be a compact subset of $\mathbb R^3$, $f$ be a function harmonic inside $X$, from Lipschitz space $C^\gamma(X)$, $0\gamma1$. A criterion for approximability of $f$ on $X$ in $C^\gamma(X)$ by functions harmonic on neighborhoods of $X$ is obtained in terms of Hausdorff content of order $1+\gamma$. The proof is completely constructive, and Vitushkin's scheme of singularities separation and approximation by parts is applied. 
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     author = {M. Ya. Mazalov},
     title = {A criterion for approximability by harmonic functions in {Lipschitz} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {144--171},
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     volume = {401},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a7/}
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M. Ya. Mazalov. A criterion for approximability by harmonic functions in Lipschitz spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 144-171. http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a7/