@article{SM_1990_66_1_a3,
author = {A. G. Korolev},
title = {On boundedness of generalized solutions of elliptic differential equations with nonpower nonlinearities},
journal = {Sbornik. Mathematics},
pages = {83--106},
year = {1990},
volume = {66},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1990_66_1_a3/}
}
A. G. Korolev. On boundedness of generalized solutions of elliptic differential equations with nonpower nonlinearities. Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 83-106. http://geodesic.mathdoc.fr/item/SM_1990_66_1_a3/
[1] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl
[2] Vishik M. I., “O razreshimosti pervoi kraevoi zadachi dlya kvazilineinykh uravnenii s bystrorastuschimi koeffitsientami v klassakh Orlicha”, DAN SSSR, 151:4 (1963), 758–761 | Zbl
[3] Dubinskii Yu. A., “Nekotorye integralnye neravenstva i razreshimost vyrozhdayuschikhsya kvazilineinykh ellipticheskikh sistem differentsialnykh uravnenii”, Matem. sb., 64(106) (1964), 458–480 | MR | Zbl
[4] Dubinskii Yu. A., “Slabaya skhodimost v ellipticheskikh i parabolicheskikh uravneniyakh”, Matem. sb., 1965, 609–642 | MR | Zbl
[5] Klimov V. S., “Teoremy vlozheniya dlya prostranstv Orlicha i ikh prilozheniya k kraevym zadacham”, Sib. matem. zhurn., 13:2 (1972), 334–348 | MR | Zbl
[6] Klimov V. S., “Kraevye zadachi v prostranstvakh Orlicha–Soboleva”, Kachestvennye i priblizhennye metody issledovaniya operatornykh uravnenii, no. 1, Yaroslavl, 1976, 75–93
[7] Klimov V. S., “K teoremam vlozheniya anizotropnykh klassov funktsii”, Matem. sb., 127(169) (1985), 198–208 | MR | Zbl
[8] Kolodii I. M., “Ob ogranichennosti obobschennykh reshenii ellipticheskikh differentsialnykh uravnenii”, Vestn. MGU. Ser. 1. Matematika, mekhanika, 1970, no. 5, 44–52 | MR | Zbl
[9] Korolev A. G., “Ob ogranichennosti obobschennykh reshenii ellipticheskikh differentsialnykh uravnenii”, UMN, 38:2 (1983), 205–206 | MR | Zbl
[10] Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, Fizmatgiz, M., 1958 | MR
[11] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR
[12] Kruzhkov S. N., “Apriornye otsenki dlya obobschennykh reshenii ellipticheskikh i parabolicheskikh uravnenii”, DAN SSSR, 150:4 (1963), 748–751 | Zbl
[13] Kruzhkov S. N., “Apriornye otsenki i nekotorye svoistva reshenii ellipticheskikh i parabolicheskikh uravnenii”, Matem. sb., 65(107) (1964), 522–570
[14] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR
[15] Lu Ven-Tuan, “K teoremam vlozheniya dlya prostranstv funktsii s chastnymi proizvodnymi, summiruemymi s razlichnymi stepenyami”, Vestnik LGU. Matematika.Mekhanika. Astronomiya., 1961, no. 7, 23–34 | MR
[16] Khardi G., Littlvud D., Poiya G., Neravenstva, IL, M., 1948
[17] Donaldson T., “Nonlinear elliptic boundari value problems in Orlicz–Sobolev spaces”, J. Diff. Eq., 10 (1971), 507–528 | DOI | MR
[18] Donaldson T., Trudinger N. S., “Orlicz–Sobolev spaces and imbedding theorems”, J. funct. anal., 1971, no. 8 | MR
[19] Evans L. S., “A new proof of local $C^{1\alpha}$ regularity for solutions of certain degenerate elliptic P. D. E.”, J. Diff. Eq., 45 (1982), 356–373 | DOI | MR | Zbl
[20] De Giorgi E., “Sulla differenziabilita e analiticita delle estremali degli integrali multipli regolari”, Mem. Acad. Sci. Torino., 3 (1957), 25–43 | MR | Zbl
[21] Gossez J., “Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coeff.”, Trans. Amer. Math. Soc., 190 (1974), 163–205 | DOI | MR | Zbl
[22] Morrey C. B., “Second order elliptic equations in several variables and Holder cintinuity”, Math. Z., 72 (1959), 146–164 | DOI | MR | Zbl
[23] Moser J., “A new proof of de Giorgi's theorem conserning the regularity problem for elliptic diff. equations”, Comm. Pure and Appl. Math., 13:3 (1960), 457–468 | DOI | MR | Zbl
[24] Nash J., “Continuity of solutions of parabolic and elliptic equations”, Amer. J. Math., 80:4 (1958), 931–954 | DOI | MR | Zbl
[25] Serrin J., “Local behavior of solutions of quasilinear equations”, Acta Math., 111:3–4 (1964), 247–302 | DOI | MR | Zbl
[26] Simon L., “Interior gradient bounds for nonuniformly elliptic equations”, Indiana Univ. Math. J., 25:9 (1976), 821–855 | DOI | MR | Zbl
[27] Talenti G., “Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces”, Annali di Mat. Pura ed Appl., 120 (1979), 159–184 | DOI | MR | Zbl
[28] Trudinger N. S., “An imbedding theorem for $\overset0H(G,\Omega)$ space”, Studia Math. (PRL), 50:1 (1974), 17–30 | MR | Zbl