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Algebra i Analiz, 2019, Volume 31, Issue 2, Pages 88–117 (Mi aa1639)  
This article is cited in 19 scientific papers (total in 19 papers)

Research Papers

Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point

Yu. A. Alkhutova, M. D. Surnachevb

a Vladimir State University
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
Full-text PDF (321 kB) Citations (19)
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Abstract: The Dirichlet problem for the $ p(x)$-Laplacian with a continuous boundary function is treated. A sufficient condition is indicated for the regularity of a boundary point, and the modulus of continuity of solutions at this point is estimated.
Keywords: Wiener criterion, boundary regularity, Dirichlet problem, variable exponent, $p(x)$-Laplacian.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.3270.2017/4.6
Russian Foundation for Basic Research 19-01-00184_а
The work was supported by the Ministry of Education and Science of the Russian Federation (grant 1.3270.2017/4.6) and Russian Foundation for Basic Research (grant 19-01-00184-a)
Received: 31.10.2018
English version:
St. Petersburg Mathematical Journal, 2019, Volume 31, Issue 2, Pages 251–271
DOI: https://doi.org/10.1090/spmj/1595
Bibliographic databases:
Document Type: Article
MSC: Primary 35J57, 35J67, 35J92; Secondary 35J15
Language: Russian
Citation: Yu. A. Alkhutov, M. D. Surnachev, “Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point”, Algebra i Analiz, 31:2 (2019), 88–117; St. Petersburg Math. J., 31:2 (2019), 251–271
Citation in format AMSBIB
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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