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Sbornik: Mathematics, 1998, Volume 189, Issue 1, Pages 1–17
DOI: https://doi.org/10.1070/sm1998v189n01ABEH000287 (Mi sm287) 		 
This article is cited in 10 scientific papers (total in 10 papers)

$L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations

Yu. A. Alkhutov

Vladimir State Pedagogical University
English version PDF (292 kB) Citations (10)
References:
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DOI: https://doi.org/10.1070/sm1998v189n01ABEH000287
Abstract: The Dirichlet problem for second-order divergence-form elliptic equations with coefficients continuous in a closed domain is considered. A necessary and sufficient condition on the boundary of a compact domain ensuring the unique $L_p$-solubility of the problem in question and also a corresponding coercive $L_p$-estimate for all $p>1$ are obtained.
Received: 18.04.1997
Russian version:
Matematicheskii Sbornik, 1998, Volume 189, Number 1, Pages 3–20
DOI: https://doi.org/10.4213/sm287
Bibliographic databases:
UDC: 517.956
MSC: Primary 35J25; Secondary 31C15
Language: English
Original paper language: Russian
Citation: Yu. A. Alkhutov, “$L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations”, Mat. Sb., 189:1 (1998), 3–20; Sb. Math., 189:1 (1998), 1–17
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:69
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