@article{SM_1985_50_2_a3,
author = {A. A. Novruzov},
title = {On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order},
journal = {Sbornik. Mathematics},
pages = {343--367},
year = {1985},
volume = {50},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1985_50_2_a3/}
}
TY - JOUR AU - A. A. Novruzov TI - On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order JO - Sbornik. Mathematics PY - 1985 SP - 343 EP - 367 VL - 50 IS - 2 UR - http://geodesic.mathdoc.fr/item/SM_1985_50_2_a3/ LA - en ID - SM_1985_50_2_a3 ER -
A. A. Novruzov. On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order. Sbornik. Mathematics, Tome 50 (1985) no. 2, pp. 343-367. http://geodesic.mathdoc.fr/item/SM_1985_50_2_a3/
[1] Cordes H. O., “Uber die erste Randwertanfgabe bei quasilinear. Differentialgleichungen zweiter Orbnung in mehr als zwei Variaben”, Math. Ann., 130 (1956), 278–312 | DOI | MR
[2] Krylov H. V., Safonov M. V., “Otsenka veroyatnosti popadaniya diffuzionnogo protsessa v mnozhestvo polozhitelnoi mery”, DAN SSSR, 245:1 (1979), 18–20 | MR
[3] Krylov H. V., Safonov M. V., “Nekotoroe svoistvo reshenii parabolicheskikh uravnenii s izmerimymi koeffitsientami”, Izvestiya AN SSSR. Seriya matem., 44 (1980), 161–175 | MR | Zbl
[4] Novruzov A. A., “Ob otsenke normy Gëldera reshenii kvazilineinykh ellipticheskikh uravnenii s razryvnymi koeffitsientami”, DAN SSSR, 253:1 (1980), 31–33 | MR | Zbl
[5] Ladyzhenskaya O. A., Uraltseva N. N., “Ob otsenkakh gëlderovskikh norm dlya reshenii kvazilineinykh ellipticheskikh uravnenii nedivergentnogo vida”, UMN, 35:4 (1980), 144–145
[6] Trudinger N. S., “Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations”, Invent. Math., 61:1 (1980), 67–69 | DOI | MR
[7] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971 | MR
[8] de Giorgi E., “Sulla differenziatbilitat l'analiticita delle estremali degli integrali multiple regolari”, ser. 3, Memorie acad. Sci. Torino, 3:1 (1957), 25–43 ; Matematika, 4, no. 6, 1960, 23–38) | MR | Zbl
[9] Nash J., “Continuity of solutions of parabolic and elliptic equations”, An. J. Math., 80 (1958), 931–954 ; Matematika, 4, no. 1, 1960, 31–52) | MR | Zbl
[10] Moser J., “A Harnack inequality for parabolic differential equations”, Comm. Pure and Appl. Math., 17:1 (1964), 101–134 | DOI | MR | Zbl
[11] Landis E. M., “Novoe dokazatelstvo teoremy De Dzhordzhi”, Trudy Mosk. matem. ob-va, 16 (1967), 219–228 | MR
[12] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR
[13] Oleinik O. A., Kruzhkov S. N., “Kvazilineinye uravneniya vtorogo poryadka so mnogimi nezavisimymi peremennymi”, UMN, 16:5 (1961), 115–155 | MR | Zbl
[14] Wiener N., “The Dirichlet problem”, Jorn. Math. Phys., Mass. Inst. Techn., 1924, no. 3, 127–146 | Zbl
[15] Keldysh M. V., “O razreshimosti i ustoichivosti zadachi Dirikhle”, UMN, 1941, no. 8, 171–231 | MR | Zbl
[16] Brelot M., “Einige nenere Untersuchungen über das Dirichletsche Problem”, Iber. Dent. Math. Vereinig, 42 (1932), 111–119
[17] Püchel W., “Die erste Randwertaufgabe der allgemeinen selbstadjungierten elliptischen Differential-gleichung zweiter Ordnung im Raum fürbeliebige Gebiete”, Math. Z., 34 (1932), 535–553 | DOI | MR
[18] Oleinik O. A., “O zadache Dirikhle dlya uravnenii ellipticheskogo tipa”, Matem. sb., 24(66) (1949), 3–14 | MR | Zbl
[19] Tautz G., “Zur Theorie der ersten Randwer taufgaben”, Math. Nachr., 2 (1949), 279–303 | DOI | MR | Zbl
[20] Herve R. M., “Recherches Axiomatiques, sur la theorie des fanctions surharmoniques ei du potentiel”, Ann. Inst. Fourier, 12 (1962), 415–571 | MR | Zbl
[21] Krylov N. V., “O pervoi kraevoi zadache dlya ellipticheskikh uravnenii”, Dif. uravneniya, 3 (1967), 315–325 | MR
[22] Landis E. M., “$s$-emkost i ee prilozheniya k issledovaniyu reshenii ellipticheskogo uravneniya 2-go poryadka s razryvnymi koeffitsientami”, Matem. sb., 76(118) (1968), 186–213 | MR | Zbl
[23] Novruzov A. A., “O regulyarnosti granichnykh tochek dlya ellipticheskogo uravneniya s nepreryvnymi koeffitsientami”, Vestn. MGU. Seriya matem. i mekhan., 1971, no. 6, 18–25 | MR | Zbl
[24] Novruzov A. A., “O module nepreryvnosti resheniya zadachi Dirikhle v regulyarnoi granichnoi tochke”, Matem. zametki, 12:1 (1972), 67–72 | MR | Zbl
[25] Littman W., Stampacchia G., Weinberger H. F., Regular points for elliptic equation with discontinuous coefficients, Univ. of Minesota, December, 1962 ; Matematika, 9, no. 2, 1965, 72–97) | MR
[26] Mazya V. G., “O povedenii vblizi granitsy resheniya zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka v divergentnoi forme”, Matem. zametki, 2:2 (1967), 209–220
[27] Mikhailov V. P., “O granichnykh znacheniyakh reshenii ellipticheskikh uravnenii”, Trudy Vses. konf. po uravneniyam s chastnymi proizvodnymi, posv. 75-letiyu so dnya rozhdeniya akad. I. G. Petrovskogo (Moskva, 27-31 yanv. 1976 g.), Izd-vo MGU, M., 1978, 160–161
[28] Gariepy R., Ziemer W. P., “A regularity condition of the boundary for solutions of quasilinear elliptic equations”, Arch. Rat. Mech. Anal., 67:1 (1977), 25–39 | DOI | MR | Zbl
[29] Landkof H. S., Osnovy sovremennei teorii potentsiala, Nauka, M., 1966 | Zbl
[30] Landis E. M., “K voprosu o edinstvennosti reshenii 1-i kraevoi zadachi dlya ellipticheskikh i parabolicheskikh uravnenii 2-go poryadka”, UMN, 33:3 (1978), 151
[31] Novruzov A. A., “O kharaktere rosta reshenii ellipticheskikh uravnenii bez printsipa maksimuma”, Issledovaniya po nekotorym voprosam teorii funktsii dlya differentsialnykh uravnenii, Baku, 1970, 84–70
[32] Landis E. M., “Nekotorye voprosy kachestvennoi teorii ellipticheskikh uravnenii”, UMN, 18:1 (1963), 3–62 | MR | Zbl
[33] Blokhina G. N., “Teoremy tipa Fragmena–Lindelëfa dlya lineinogo ellipticheskogo uravneniya vtorogo poryadka”, DAN SSSR, 162:4 (1965), 727–730 | Zbl
[34] Ivanovich M. D., “O kharaktere nepreryvnosti reshenii lineinykh ellipticheskikh uravnenii vtorogo poryadka”, Vestn. MGU. Seriya matem. i mekhan., 1966, no. 3, 37–47 | Zbl
[35] Novruzov A. A., “O neobkhodimom i dostatochnom uslovii regulyarnosti granichnykh tochek dlya kvazilineinykh ellipticheskikh uravnenii 2-go poryadka”, DAN SSSR, 233:4 (1977), 547–550 | MR | Zbl
[36] Mamedov I. T., “Ob apriornoi otsenke normy Gëldera reshenii kvazilineinykh parabolicheskikh uravnenii s razryvnymi koeffitsientami”, DAN SSSR, 252:5 (1980), 1052–1054 | MR | Zbl
[37] Mazya V. G., “O regulyarnosti na granitse reshenii ellipticheskikh uravnenii i konformnogo otobrazheniya”, DAN SSSR, 152:6 (1963), 1297–1300