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

This article is cited in 5 scientific papers (total in 5 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

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.

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

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 434–452

Bibliographic databases:

UDC: 517.956
Received: 26.07.2016

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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\paper On the entropy solution to an elliptic problem in anisotropic Sobolev--Orlicz spaces
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 429--447
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\crossref{https://doi.org/10.7868/S0044466917030103}
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\crossref{https://doi.org/10.1134/S0965542517030101}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kozhevnikova L.M., “On Solutions of Anisotropic Elliptic Equations With Variable Exponent and Measure Data”, Complex Var. Elliptic Equ.  crossref  isi
    2. 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  mathnet  crossref
    3. 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  mathnet  crossref  isi
    4. F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents”, Sb. Math., 209:5 (2018), 714–738  mathnet  crossref  crossref  adsnasa  isi  elib
    5. L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446  mathnet  crossref  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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