Criterion of uniform approximability by harmonic functions on compact sets in a"e3

For a function continuous on a compact set X aS, a"e(3) 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. DOI: 10.1134/S008154381208010X