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 
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/
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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.

[1] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971 | MR

[2] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

[3] Grigoryan A. A., “Ob odnoi liuvillevoi teoreme na rimanovom mnogoobrazii”, Tr. Tbil. un-ta. matem. mekh., astron., 232–233 (1982), 49–77 | MR

[4] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[5] Khadviger G., Lektsii ob ob'eme ploschadi poverkhnosti i izoperimetrii, Nauka, M., 1966

[6] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[7] Mazya V. G., “O regulyarnosti na granitse reshenii ellipticheskikh uravnenii i konformnogo otobrazheniya”, DAN SSSR, 152:6 (1963), 1297–1300

[8] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR