@article{ZVMMF_2017_57_3_a6,
author = {L. M. Kozhevnikova},
title = {On the entropy solution to an elliptic problem in anisotropic {Sobolev{\textendash}Orlicz} spaces},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {429--447},
year = {2017},
volume = {57},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a6/}
}
TY - JOUR AU - L. M. Kozhevnikova TI - On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2017 SP - 429 EP - 447 VL - 57 IS - 3 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a6/ LA - ru ID - ZVMMF_2017_57_3_a6 ER -
%0 Journal Article %A L. M. Kozhevnikova %T On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2017 %P 429-447 %V 57 %N 3 %U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a6/ %G ru %F ZVMMF_2017_57_3_a6
L. M. Kozhevnikova. On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 429-447. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a6/
[1] Brezis H., “Semilinear equations in $R^N$ without condition at infnity”, Appl. Math. Optim., 12:3 (1984), 271–282 | DOI | MR | Zbl
[2] Boccardo L., Gallouet T., Vazquez J. L., “Nonlinear elliptic equaitons in $R^N$ without growth restrictions on the data”, J. Differential Equations, 105:2 (1993), 334–363 | DOI | MR | Zbl
[3] Bendahmane M., Karlsen K., “Nonlinear anisotropic elliptic and parabolic equations in $R^N$ with advection and lower order terms and locally integrable data”, Potential Analysis, 22:3 (2005), 207–227 | DOI | MR | Zbl
[4] Boccardo L., Gallouet Th., “Nonlinear elliptic equations with right-hand side measures”, Comm. Partial Differential Equations, 17:3–4 (1992), 641–655 | MR | Zbl
[5] Boccardo L., Gallouet Th., Marcellini P., “Anisotropic equations in $L^1$”, Differential Integral Equations, 9:1 (1996), 209–212 | MR | Zbl
[6] Benilan Ph., Boccardo L., Galluet Th., Pierre M., Vazquez J. L., “An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations”, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 22:2 (1995), 241–273 | MR | Zbl
[7] Boccardo L., “Some nonlinear Dirichlet problems in $L^1$ involving lower order terms in divergence form”, Pitman Res. Notes Math. Ser., 350, 1996, 43–57 | MR | Zbl
[8] Kovalevskii A. A., “Apriornye svoistva reshenii nelineinykh uravnenii s vyrozhdayuscheisya koertsitivnostyu i $L^1$-dannymi”, Sovremennaya matem. Fundamentalnye napravl., 16, 2006, 47–67
[9] Benkirane A., Bennouna J., “Existence of entropy solutions for some elliptic problems involving derivatives of nonlinear terms in Orlicz spaces”, Abstr. Appl. Anal., 7:2 (2002), 85–102 | DOI | MR | Zbl
[10] Aharouch L., Bennouna J., Touzani A., “Existence of renormalized solution of some elliptic problems in Orlicz spaces”, Rev. Mat. Complut., 22:1 (2009), 91–110 | DOI | MR | Zbl
[11] Gwiazda P., Wittbold P., Wróblewska A., Zimmermann A., Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces, PhD programme: Mathematical methods in natural sciences (MMNS). Preprint No 2011-013, 2011 | MR
[12] Rutitskii Ya. B., Krasnoselskii M. A., Vypuklye funktsii i prostranstva Orlicha, Fizmatlit, M., 1958
[13] Korolev A. G., “Teoremy vlozheniya anizotropnykh prostranstv Soboleva–Orlicha”, Vestn. Mosk. univ. Ser. 1, 1983, no. 1, 32–37
[14] Gossez J. P., “Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients”, Trans. Amer. Math. Soc., 190 (1974), 163–206 | DOI | MR
[15] Lions Zh. L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972
[16] Kozhevnikova L. M., Khadzhi A. A., “Suschestvovanie reshenii anizotropnykh ellipticheskikh uravnenii s nestepennymi nelineinostyami v neogranichennykh oblastyakh”, Matem. sb., 206:8 (2015), 99–126 | DOI | Zbl
[17] Kozhevnikova L. M., Khadzhi A. A., “O resheniyakh ellipticheskikh uravnenii s nestepennymi nelineinostyami v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-matem. nauki, 19 (2015), 44–62 | DOI