Geodesic
On exceptional sets on the boundary and uniqueness of a solution of the second and third boundary value problems for an elliptic equation
Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 351-366 
S. V. Gaidenko. On exceptional sets on the boundary and uniqueness of a solution of the second and third boundary value problems for an elliptic equation. Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 351-366. http://geodesic.mathdoc.fr/item/SM_1986_53_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The question is studied of the uniqueness of a solution of the third (in particular, the second) boundary value problem for a linear elliptic equation of second order in the case where the boundary conditions are prescribed everywhere except on some exceptional set of points of the boundary. In terms of Hausdorff measure, restrictions on the exceptional set are obtained under which the space $L_p$ is a uniqueness class for the problem considered. Bibliography: 9 titles.

[1] Mikheeva E. A., “O edinstvennosti resheniya vtoroi i tretei kraevykh zadach dlya ellipticheskogo uravneniya vtorogo poryadka”, DAN SSSR, 167:5 (1966), 978–981 | Zbl

[2] Moiseev E. I., “O zadache Neimana v kusochno-gladkikh oblastyakh”, Differents. uravneniya, 7:9 (1971), 1655–1666 | MR | Zbl

[3] Moiseev E. I., “O suschestvennykh i nesuschestvennykh granichnykh mnozhestvakh zadachi Neimana”, Differents. uravneniya, 9:5 (1973), 901–911 | MR | Zbl

[4] Gaidenko S. V., “Ob isklyuchitelnykh mnozhestvakh na granitse i edinstvennosti reshenii zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 111(153) (1980), 116–134 | MR | Zbl

[5] Guschin A. K, Mikhailov V. P., “O povedenii vblizi granitsy resheniya tretei kraevoi zadachi dlya ellipticheskogo uravneniya vtorogo poryadka”, Kompleksnyi analiz i ego prilozheniya, Nauka, M., 1978, 193–202

[6] Mikhailov V. P., “O granichnykh znacheniyakh reshenii ellipticheskikh uravnenii v oblastyakh s gladkoi granitsei”, Matem. sb., 101(143) (1976), 163–188

[7] Koshelev A. I., “Apriornye otsenki v $L_p$ i obobschennye resheniya ellipticheskikh uravnenii i sistem”, UMN, 13:4 (1958), 29–88 | MR

[8] Browder F. E., “Estimaties and existence theorems for elliptic boundary value problems”, Proc. Nat. Acad. Sci. USA, 45:3 (1959), 365–372 | DOI | MR | Zbl

[9] Karleson L., Izbrannye problemy teorii isklyuchitelnykh mnozhestv, Mir, M., 1971 | MR | Zbl