Geodesic
Conditions for $C^m$-approximability of functions by solutions of elliptic equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 6, pp. 1023-1068

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This paper is a survey of results obtained over the past 20–30 years in the qualitative theory of approximation of functions by holomorphic, harmonic, and polyanalytic functions (and, in particular, by corresponding polynomials) in the norms of Whitney-type spaces $C^m$ on compact subsets of Euclidean spaces. Bibliography: 120 titles.
Keywords: $C^m$-approximation by holomorphic, harmonic, and polyanalytic functions; $C^m$-analytic and $C^m$-harmonic capacity; $s$-dimensional Hausdorff content; Vitushkin localization operator; Nevanlinna domains; Dirichlet problem. 
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     title = {Conditions for $C^m$-approximability of functions by solutions of elliptic equations},
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M. Ya. Mazalov; P. V. Paramonov; K. Yu. Fedorovskiy. Conditions for $C^m$-approximability of functions by solutions of elliptic equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 6, pp. 1023-1068. http://geodesic.mathdoc.fr/item/RM_2012_67_6_a2/