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Sbornik: Mathematics, 2020, Volume 211, Issue 12, Pages 1737–1776
DOI: https://doi.org/10.1070/SM9371 (Mi sm9371) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Renormalized solutions of elliptic equations with variable exponents and general measure data

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 (744 kB) Citations (2) Russian version article
References:
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DOI: https://doi.org/10.1070/SM9371
Abstract: A class of second-order elliptic equations with variable nonlinearity exponents and the right-hand side in the form of the general Radon measure with finite total variation is considered. The existence of a renormalized solution of the Dirichlet problem is proved as a consequence of stability with respect to the convergence of the right-hand side of the equation.
Bibliography: 37 titles.
Keywords: quasilinear elliptic equation, renormalized solution, Radon measure, variable exponent, Dirichlet problem.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00428-a
This study was supported by the Russian Foundation for Basic Research (project no. 18-01-00428-а).
Received: 20.01.2020 and 07.04.2020
Bibliographic databases:
Document Type: Article
UDC: 517.956.25
MSC: Primary 35J62; Secondary 35J92
Language: English
Original paper language: Russian
Citation: L. M. Kozhevnikova, “Renormalized solutions of elliptic equations with variable exponents and general measure data”, Sb. Math., 211:12 (2020), 1737–1776
Citation in format AMSBIB
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\by L.~M.~Kozhevnikova
\paper Renormalized solutions of elliptic equations with~variable exponents and general measure data
\jour Sb. Math.
\yr 2020
\vol 211
\issue 12
\pages 1737--1776
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Linking options:
  • https://www.mathnet.ru/eng/sm9371
  • https://doi.org/10.1070/SM9371
  • https://www.mathnet.ru/eng/sm/v211/i12/p83
    • This publication is cited in the following 2 articles:
    1. A. P. Kashnikova, L. M. Kozhevnikova, “Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces”, Sb. Math., 213:4 (2022), 476–511  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Giri R.K., Choudhuri D., “Reduced Limit Approach to Semilinear Partial Differential Equations (Pdes) Involving the Fractional Laplacian With Measure Data”, Turk. J. Math., 2021  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:452
    Russian version PDF:92
    English version PDF:37
    References:80
    First page:17
     
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