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Mat. Sb., 1998, Volume 189, Number 1, Pages 3–20 (Mi msb287)  

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

Full text: PDF file (322 kB)
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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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    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. 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  crossref  mathscinet  zmath  isi  scopus  scopus
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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  mathnet  crossref
    4. A. K. Gushchin, “$L_p$-estimates for solutions of second-order elliptic equation Dirichlet problem”, Theoret. and Math. Phys., 174:2 (2013), 209–219  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. K. Guschin, “O zadache Dirikhle dlya ellipticheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 19–43  mathnet  crossref  zmath  elib
    6. 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  mathnet  crossref  crossref  isi  elib
    7. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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