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Differ. Uravn., 1976, Volume 12, Number 10, Pages 1877–1891 (Mi de2898)  

This article is cited in 23 scientific papers (total in 23 papers)

Partial Differential Equations

The Dirichlet problem for a second order elliptic equation

V. P. Mikhailov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Full text: PDF file (1359 kB)

Bibliographic databases:
UDC: 517.946
Received: 23.06.1976

Citation: V. P. Mikhailov, “The Dirichlet problem for a second order elliptic equation”, Differ. Uravn., 12:10 (1976), 1877–1891

Citation in format AMSBIB
\Bibitem{Mik76}
\by V.~P.~Mikhailov
\paper The Dirichlet problem for a second order elliptic equation
\jour Differ. Uravn.
\yr 1976
\vol 12
\issue 10
\pages 1877--1891
\mathnet{http://mi.mathnet.ru/de2898}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=442461}
\zmath{https://zbmath.org/?q=an:0336.35035}


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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. A. K. Gushchin, V. P. Mikhailov, “On boundary values in $L_p$, $p>1$, of solutions of elliptic equations”, Math. USSR-Sb., 36:1 (1980), 1–19  mathnet  crossref  mathscinet  zmath  isi
    2. S. V. Gaidenko, “On exceptional sets on the boundary and the uniqueness of solutions of the Dirichlet problem for a second order elliptic equation”, Math. USSR-Sb., 39:1 (1981), 107–123  mathnet  crossref  mathscinet  zmath  isi
    3. A. K. Gushchin, “On the Dirichlet problem for a second-order elliptic equation”, Math. USSR-Sb., 65:1 (1990), 19–66  mathnet  crossref  mathscinet  zmath
    4. A. K. Gushchin, V. P. Mikhailov, “On solvability of nonlocal problems for a second-order elliptic equation”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 101–136  mathnet  crossref  mathscinet  zmath  isi
    5. A. K. Gushchin, “Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation”, Sb. Math., 189:7 (1998), 1009–1045  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. K. Gushchin, “A condition for the compactness of operators in a certain class and its application to the analysis of the solubility of non-local problems for elliptic equations”, Sb. Math., 193:5 (2002), 649–668  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. A. K. Gushchin, “A strengthening of the interior Hölder continuity property for solutions of the Dirichlet problem for a second-order elliptic equation”, Theoret. and Math. Phys., 157:3 (2008), 1655–1670  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. Zh. Dumanyan, “Dirichlet weight integral estimation to Dirichlet problem solution for the general second order elliptic equations”, Uch. zapiski EGU, ser. Fizika i Matematika, 2009, no. 3, 10–21  mathnet
    9. V. P. Mikhailov, “Existence of boundary values of polyharmonic functions”, Sb. Math., 201:5 (2010), 735–757  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. A. K. Guschin, “Otsenki resheniya zadachi Dirikhle s granichnoi funktsiei iz $L_p$”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 53–67  mathnet  crossref  elib
    11. V. Zh. Dumanyan, “Solvability of the Dirichlet problem for a general second-order elliptic equation”, Sb. Math., 202:7 (2011), 1001–1020  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. A. K. Gushchin, “The Dirichlet problem for a second-order elliptic equation with an $L_p$ boundary function”, Sb. Math., 203:1 (2012), 1–27  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. 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
    14. V. P. Mikhailov, “O suschestvovanii granichnykh znachenii u reshenii ellipticheskikh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 97–105  mathnet  crossref
    15. 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
    16. V. Zh. Dumanyan, “Solvability of the Dirichlet problem for second-order elliptic equations”, Theoret. and Math. Phys., 180:2 (2014), 917–931  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    17. L. M. Kozhevnikova, A. A. Khadzhi, “Existence of solutions of anisotropic elliptic equations with nonpolynomial nonlinearities in unbounded domains”, Sb. Math., 206:8 (2015), 1123–1149  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. A. K. Gushchin, “Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation”, Sb. Math., 206:10 (2015), 1410–1439  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. 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
    20. 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
    21. A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    22. A. K. Gushchin, “The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation”, Sb. Math., 209:6 (2018), 823–839  mathnet  crossref  crossref  adsnasa  isi  elib
    23. A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64  mathnet  crossref  crossref  isi  elib  elib
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