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This article is cited in 7 scientific papers (total in 7 papers)
$L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations
Yu. A. Alkhutov
Vladimir State Pedagogical University
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.
DOI:
https://doi.org/10.4213/sm287
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English version:
Sbornik: Mathematics, 1998, 189:1, 1–17
Bibliographic databases:
   
UDC:
517.956
MSC: Primary 35J25; Secondary 31C15
Received: 18.04.1997
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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http://mi.mathnet.ru/eng/msb287https://doi.org/10.4213/sm287 http://mi.mathnet.ru/eng/msb/v189/i1/p3
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This publication is cited in the following articles:
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Miyazaki, Y, “The L-P resolvents of second-order elliptic operators of divergence form under the Dirichlet condition”, Journal of Differential Equations, 206:2 (2004), 353
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Yu. A. Alkhutov, A. N. Gordeev, “$L_p$-solubility of the Dirichlet problem for the heat operator”, Russian Math. Surveys, 64:1 (2009), 131–133
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A. K. Guschin, “$L_p$-otsenki nekasatelnoi maksimalnoi funktsii dlya reshenii ellipticheskogo uravneniya vtorogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 53–69
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A. K. Gushchin, “$L_p$-estimates for solutions of second-order elliptic equation Dirichlet problem”, Theoret. and Math. Phys., 174:2 (2013), 209–219
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A. K. Guschin, “O zadache Dirikhle dlya ellipticheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 19–43
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A. K. Gushchin, “V.A. Steklov's work on equations of mathematical physics and development of his results in this field”, Proc. Steklov Inst. Math., 289 (2015), 134–151
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A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
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