L. M. Kozhevnikova, “On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 429–447; Comput. Math. Math. Phys., 57:3 (2017), 434

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 3, Pages 429–447
DOI: https://doi.org/10.7868/S0044466917030103 (Mi zvmmf10535)

This article is cited in 13 scientific papers (total in 13 papers)

On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces

L. M. Kozhevnikova^ab

^a Elabuga Institute, Kazan Federal University, Elabuga, Russia
^b Sterlitamak Branch, Bashkir State University, Sterlitamak, Russia

Full-text PDF (289 kB) Citations (13)

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DOI: https://doi.org/10.7868/S0044466917030103

Abstract: For a certain class of anisotropic elliptic equations with the right-hand side from

L_{1}

$L_1$ in an arbitrary unbounded domains, the Dirichlet problem with an inhomogeneous boundary condition is considered. The existence and uniqueness of the entropy solution in anisotropic Sobolev–Orlicz spaces are proven.

Key words: anisotropic elliptic equation, entropy solution, uniqueness of solution, existence of solution, Sobolev–Orlicz space,

N

$N$ -functions.

Received: 26.07.2016

English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 3, Pages 434–452
DOI: https://doi.org/10.1134/S0965542517030101

Bibliographic databases:

Document Type: Article

UDC: 517.956

Language: Russian

Citation: L. M. Kozhevnikova, “On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 429–447; Comput. Math. Math. Phys., 57:3 (2017), 434–452

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/zvmmf10535

https://www.mathnet.ru/eng/zvmmf/v57/i3/p429

This publication is cited in the following 13 articles:

Zengfei Chen, Bingliang Shen, “The Existence of Entropy Solutions for a Class of Parabolic Equations”, Mathematics, 11:17 (2023), 3753
Omar Benslimane, Ahmed Aberqi, Jaouad Bennouna, “On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space”, AJMS, 29:1 (2023), 29
Rabab Elarabi, Badr Lahmi, Hakima Ouyahya, “On some nonlinear elliptic problems in anisotropic Orlicz–Sobolev spaces”, Adv. Oper. Theory, 8:2 (2023)
A. P. Kashnikova, L. M. Kozhevnikova, “Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces”, Sb. Math., 213:4 (2022), 476–511
Omar Benslimane, Ahmed Aberqi, Jaouad Bennouna, “Study of some nonlinear elliptic equation with non-polynomial anisotropic growth”, Adv. Oper. Theory, 7:3 (2022)
O. Benslimane, A. Aberqi, J. Bennouna, “Existence and uniqueness of entropy solution of a nonlinear elliptic equation in anisotropic Sobolev-Orlicz space”, Rend. Circ. Mat. Palermo, 70:3 (2021), 1579–1608
L. M. Kozhevnikova, “On solutions of anisotropic elliptic equations with variable exponent and measure data”, Complex Var. Elliptic Equ., 65:3 (2020), 333–367
L. M. Kozhevnikova, “Equivalence of entropy and renormalized solutions of the anisotropic elliptic problem in unbounded domains with measure data”, Russian Math. (Iz. VUZ), 64:1 (2020), 25–39
O. Benslimane, A. Aberqi, J. Bennouna, “The existence and uniqueness of an entropy solution to unilateral Orlicz anisotropic equations in an unbounded domain”, Axioms, 9:3 (2020), 109
L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446
T. R. Gadyl'shin, F. Kh. Mukminov, “Perturbation of second order nonlinear equation by delta-like potential”, Ufa Math. J., 10:2 (2018), 31–43
F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents”, Sb. Math., 209:5 (2018), 714–738
L. M. Kozhevnikova, “Ob entropiinykh resheniyakh anizotropnykh ellipticheskikh uravnenii s peremennymi pokazatelyami nelineinostei v neogranichennykh oblastyakh”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 3, Rossiiskii universitet druzhby narodov, M., 2017, 475–493

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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