Geodesic
Some estimates of the solution of the Neumann problem, and the modulus of continuity of a conformal mapping
Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 219-228

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New estimates are established for the Hölder norm of generalized solutions of the Neumann problem in a planar domain. The estimates obtained for the solution of the Neumann problem are used to investigate the modulus of continuity of a conformal mapping near the boundary. Bibliography: 8 titles. 
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     author = {N. S. Nadirashvili},
     title = {Some estimates of the solution of the {Neumann} problem, and the modulus of continuity of a conformal mapping},
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N. S. Nadirashvili. Some estimates of the solution of the Neumann problem, and the modulus of continuity of a conformal mapping. Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 219-228. http://geodesic.mathdoc.fr/item/SM_1989_63_1_a14/