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

This article is cited in 5 scientific papers (total in 5 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
  • http://mi.mathnet.ru/eng/msb/v210/i3/p131

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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. Abdellaoui M., “Generalized Solutions For a Class of Nonlinear Parabolic Problems With Irregular Data in Unbounded Domains”, Adv. Oper. Theory  crossref  mathscinet  isi
    2. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. 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  mathnet  crossref  crossref  isi
    4. A. K. Gushchin, “Extensions of the space of continuous functions and embedding theorems”, Sb. Math., 211:11 (2020), 1551–1567  mathnet  crossref  crossref  mathscinet  isi  elib
    5. L. M. Kozhevnikova, “Renormalized solutions of elliptic equations with variable exponents and general measure data”, Sb. Math., 211:12 (2020), 1737–1776  mathnet  crossref  crossref  mathscinet  isi  elib
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