On the question of the uniqueness of the solution of the second boundary value problem for second order elliptic equations
Sbornik. Mathematics, Tome 50 (1985) no. 2, pp. 325-341 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A common method is given for investigating.classical solutions of various boundary value problems for second order elliptic equations: the second boundary value problem in domains with nonsmooth boundaries, the second boundary value problem for degenerating elliptic equations, and problems with oblique derivatives. Existence and uniqueness theorems for classical solutions are proved. Bibliography: 15 titles.
@article{SM_1985_50_2_a2,
     author = {N. S. Nadirashvili},
     title = {On the question of the uniqueness of the solution of the second boundary value problem for second order elliptic equations},
     journal = {Sbornik. Mathematics},
     pages = {325--341},
     year = {1985},
     volume = {50},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_50_2_a2/}
}
TY  - JOUR
AU  - N. S. Nadirashvili
TI  - On the question of the uniqueness of the solution of the second boundary value problem for second order elliptic equations
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 325
EP  - 341
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1985_50_2_a2/
LA  - en
ID  - SM_1985_50_2_a2
ER  - 
%0 Journal Article
%A N. S. Nadirashvili
%T On the question of the uniqueness of the solution of the second boundary value problem for second order elliptic equations
%J Sbornik. Mathematics
%D 1985
%P 325-341
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1985_50_2_a2/
%G en
%F SM_1985_50_2_a2
N. S. Nadirashvili. On the question of the uniqueness of the solution of the second boundary value problem for second order elliptic equations. Sbornik. Mathematics, Tome 50 (1985) no. 2, pp. 325-341. http://geodesic.mathdoc.fr/item/SM_1985_50_2_a2/

[1] Girand G., “Généralizations des problémes sur les opérations du type elliptique”, Bull. Math. Soc. France, 1932, no. 56, 316–352

[2] Oleinik O. A., “O zadache Dirikhle dlya uravnenii ellipticheskogo tipa”, Matem. sb., 24(66) (1949), 3–14 | MR | Zbl

[3] Hopf E., “A remark on linear elliptic differential equations of second order”, Proc. Am. Math. Soc. 3, 1952, 791–793 | DOI | MR | Zbl

[4] Keldysh M., Lavrentev M., “O edinstvennosti zadachi Neimana”, DAN SSSR, 16:3 (1937), 151–152

[5] Smirnov V. I., Kurs vysshei matematiki, t. 4, ch. II, Nauka, M., 1981

[6] Kamynin L. I., Khimchenko B. N., “K issledovaniyu o printsipe maksimuma”, DAN SSSR, 240:4 (1978), 774–777 | MR | Zbl

[7] Nadirashvili N. S., “Lemma o vnutrennei proizvodnoi i edinstvennost resheniya 2-i kraevoi zadachi dlya ellipticheskikh uravnenii vtorogo poryadka”, DAN SSSR, 261:4 (1981), 804–808 | MR | Zbl

[8] Aleksandrov A. D., “Issledovanie o printsipe maksimuma, I”, Izv. vuzov. Matem., 1958, no. 5, 126–157 | MR | Zbl

[9] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR

[10] Jerison D. S., Kenig C. E., “The Neuman problem on Lipschitz domains”, Bull. Amer. Math. Soc., 4:2 (1981), 203–207 | DOI | MR | Zbl

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

[12] Dahlberg B. E. J., “Estimates of Harmonic Measure”, Arch. Rat. Mech. An., 65 (1977), 275–288 | DOI | MR | Zbl

[13] Jerison D. S., Kenig C. E., “The Dirichlet problem in non-smooth domains”, Ann. of Math., 113 (1981), 367–382 | DOI | MR | Zbl

[14] Fabes E. B., Jodeit M., Riviere N. M., “Potential techniques for boundary value problems on $C^1$-domains”, Acta Math., 141:3–4 (1978), 165–186 | DOI | MR | Zbl

[15] Gilbarg D., Hörmander L., “Intermediate Schauder Estimates”, Arch. Rat. Mech. An., 74 (1980), 197–218 | DOI | MR