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Mat. Sb., 2019, Volume 210, Number 3, Pages 131–161 (Mi msb9078)  

This article is cited in 2 scientific papers (total in 2 papers)

Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents

L. M. Kozhevnikovaab

a Sterlitamak Branch of Bashkir State University, Sterlitamak, Russia
b Elabuga Branch of Kazan (Volga region) Federal University, Elabuga, Russia

Abstract: The Dirichlet problem is considered in arbitrary domains for a class of second-order anisotropic elliptic equations with variable nonlinearity exponents and right-hand sides in $L_1$. It is proved that an entropy solution exists in anisotropic Sobolev spaces with variable exponent. It is proved that the entropy solution obtained is a renormalized solution of the problem under consideration.
Bibliography: 37 titles.

Keywords: anisotropic elliptic equation, entropy solution, renormalized solution, existence of a solution, variable exponent, Dirichlet problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00428-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-01-00428-a).


DOI: https://doi.org/10.4213/sm9078

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English version:
Sbornik: Mathematics, 2019, 210:3, 417–446

Bibliographic databases:

UDC: 517.956.25
MSC: 35J25, 35J60
Received: 31.01.2018 and 22.02.2018

Citation: L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Mat. Sb., 210:3 (2019), 131–161; Sb. Math., 210:3 (2019), 417–446

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm9078
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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. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  isi  elib
    2. L. M. Kozhevnikova, “Ekvivalentnost entropiinykh i renormalizovannykh reshenii anizotropnoi ellipticheskoi zadachi v neogranichennykh oblastyakh s dannymi v vide mery”, Izv. vuzov. Matem., 2020, no. 1, 30–45  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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