RUS  ENG
Full version
JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki

Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 429–447 (Mi zvmmf10535)

On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces
L. M. Kozhevnikova

References

1. Brezis H., “Semilinear equations in $R^N$ without condition at infnity”, Appl. Math. Optim., 12:3 (1984), 271–282  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
4. Boccardo L., Gallouet Th., “Nonlinear elliptic equations with right-hand side measures”, Comm. Partial Differential Equations, 17:3–4 (1992), 641–655  mathscinet  zmath
5. Boccardo L., Gallouet Th., Marcellini P., “Anisotropic equations in $L^1$”, Differential Integral Equations, 9:1 (1996), 209–212  mathscinet  zmath
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  mathscinet  zmath
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  mathscinet  zmath
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  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
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 № 2011-013, 2011  mathscinet
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  crossref  mathscinet
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  mathnet  crossref  zmath  elib
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  mathnet  crossref


© Steklov Math. Inst. of RAS, 2026