Geodesic
Some qualitative properties of solutions of the mixed problem for equations of elliptic type
Sbornik. Mathematics, Tome 50 (1985) no. 1, pp. 163-176 
A. I. Ibragimov. Some qualitative properties of solutions of the mixed problem for equations of elliptic type. Sbornik. Mathematics, Tome 50 (1985) no. 1, pp. 163-176. http://geodesic.mathdoc.fr/item/SM_1985_50_1_a10/
@article{SM_1985_50_1_a10,
     author = {A. I. Ibragimov},
     title = {Some qualitative properties of solutions of the mixed problem for equations of elliptic type},
     journal = {Sbornik. Mathematics},
     pages = {163--176},
     year = {1985},
     volume = {50},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_50_1_a10/}
}
TY  - JOUR
AU  - A. I. Ibragimov
TI  - Some qualitative properties of solutions of the mixed problem for equations of elliptic type
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 163
EP  - 176
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1985_50_1_a10/
LA  - en
ID  - SM_1985_50_1_a10
ER  - 
%0 Journal Article
%A A. I. Ibragimov
%T Some qualitative properties of solutions of the mixed problem for equations of elliptic type
%J Sbornik. Mathematics
%D 1985
%P 163-176
%V 50
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1985_50_1_a10/
%G en
%F SM_1985_50_1_a10

Voir la notice de l'article provenant de la source Math-Net.Ru

The existence and Hölder property in the closure of the domain is proved for the weak and generalized solutions of the Zaremba problem, provided that the domain satisfies a condition of isoperimetric type. Figures: 2. Bibliography: 21 titles.

[1] De Giorgi E., “Sulla differenziabilitàe l'analicità delle ertremali degli integrali multipli regolari”, Ser. 3, Memorie delle Ace. Sci. Torino, 3:1 (1957), 25–43 | MR | Zbl

[2] Nash J., “Continuiti of solutions of parabolic and elliptic equations”, Amer. J. Math., 80:4 (1958), 931–954 | DOI | MR | Zbl

[3] Moser J., “A new proof of de Giorgis theorem concerning the regulariti for elliptic differential equations”, Comm. Pur. Appl. Math., 13:3 (1960), 457–468 | DOI | MR | Zbl

[4] Landis E. M., “Novoe dokazatelstvo teoremy de Dzhorzhi”, Trudy Mosk. matem. ob-va, 16 (1967), 219–228 | MR

[5] Novruzov A. A., “K teorii tretei kraevoi zadachi dlya lineinykh ellipticheskikh uravnenii 2-go poryadka”, DAN SSSR, 261:2 (1981), 278–282 | MR | Zbl

[6] Guschin A. K., “Ob otsenkakh reshenii kraevykh zadach dlya parabolicheskogo uravneniya vtorogo poryadka”, Trudy MIAN SSSR, 126 (1973), 5–45 | Zbl

[7] Guschin A. K., “Ob otsenkakh Dirikhle v neogranichennykh oblastyakh”, Matem. sb., 99 (141) (1976), 282–294 | Zbl

[8] Guschin A. K., “Nekotorye svoistva obobschennogo resheniya vtoroi kraevoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 97 (139) (1975), 242–261 | Zbl

[9] Mazya V. G., “O zadache Neimana v oblastyakh s neregulyarnymi granitsami”, Sib. matem. zh., XI:6 (1968), 1322–1350

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

[11] Zaremba S., “Ob odnoi smeshannoi zadache, otnosyascheisya k uravneniyu Laplasa”, UMN, 1:3–4(13–14) (1946), 125–146 | MR | Zbl

[12] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[13] Agmon S., Duglis A., Nirenberg L., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, M., 1962

[14] Kerimov T. M., “Kriterii regulyarnosti granichnoi tochki otnositelno smeshannoi zadachi dlya ellipticheskogo uravneniya vtorogo poryadka”, DAN AzSSR, XXXVII:9 (1981), 10–14 | MR

[15] Kondratev V. A., “O gëlderovosti v zamykanii oblasti reshenii smeshannoi zadachi dlya ellipticheskikh uravnenii vysokogo poryadka”, UMN, 37:4 (1982), 104–105 | MR

[16] Landis E. M., “O slabom neravenstve Kharnaka dlya pochti lineinogo ellipticheskogo uravneniya”, Trudy Tbiliskogo un-ta, matem. mekh. astr., 232–233 (1982), 159–184 | MR | Zbl

[17] Grigoryan A. S., “O teoremakh tipa Liuvillya na polnom rimanovom mnogoobrazii”, Tam zhe, 120–143

[18] Ladyzhenskaya O. A., Uraltseva P. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Fizmatgiz, M., 1964

[19] Kronrod A. S., “O funktsiyakh dvukh peremennykh”, UMN, 5:I (1950), 24–134 | MR | Zbl

[20] Mazya V. G., “Nekotorye otsenki reshenii ellipticheskikh uravnenii vtorogo poryadka”, DAN SSSR, 137:5 (1961), 1057–1059

[21] Mazya V. G., “O slabykh resheniyakh zadach Dirikhle i Neimana”, Trudy Mosk. matem. ob-va, 20 (1969), 137–172