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Sbornik: Mathematics, 2019, Volume 210, Issue 3, Pages 417–446
DOI: https://doi.org/10.1070/SM9078 (Mi sm9078) 		 
This article is cited in 14 scientific papers (total in 14 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
English version PDF (637 kB) Citations (14) Russian version article
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DOI: https://doi.org/10.1070/SM9078
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).
Received: 31.01.2018 and 22.02.2018
Bibliographic databases:
Document Type: Article
UDC: 517.956.25
MSC: 35J25, 35J60
Language: English
Original paper language: Russian
Citation: L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446
Citation in format AMSBIB
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\by L.~M.~Kozhevnikova
\paper Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents
\jour Sb. Math.
\yr 2019
\vol 210
\issue 3
\pages 417--446
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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