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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. Kozhevnikovaab

a Elabuga Institute, Kazan Federal University, Elabuga, Russia
b Sterlitamak Branch, Bashkir State University, Sterlitamak, Russia
References:
Abstract: For a certain class of anisotropic elliptic equations with the right-hand side from $L_1$ 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, $N$-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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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:78
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