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Mat. Sb. (N.S.), 1982, Volume 119(161), Number 1(9), Pages 48–77 (Mi msb2836)  

This article is cited in 19 scientific papers (total in 19 papers)

On boundary values of solutions of elliptic equations in domains with Lyapunov boundary

I. M. Petrushko


Abstract: The question of boundary values for solutions of elliptic equations in domains with Lyapunov boundary is investigated.
Bibliography: 7 titles.

Full text: PDF file (1199 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1984, 47:1, 43–72

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J25, 35J67; Secondary 35A05, 35B45, 35D99, 46E35
Received: 15.01.1982

Citation: I. M. Petrushko, “On boundary values of solutions of elliptic equations in domains with Lyapunov boundary”, Mat. Sb. (N.S.), 119(161):1(9) (1982), 48–77; Math. USSR-Sb., 47:1 (1984), 43–72

Citation in format AMSBIB
\Bibitem{Pet82}
\by I.~M.~Petrushko
\paper On~boundary values of solutions of elliptic equations in domains with Lyapunov boundary
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 119(161)
\issue 1(9)
\pages 48--77
\mathnet{http://mi.mathnet.ru/msb2836}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=672409}
\zmath{https://zbmath.org/?q=an:0525.35040|0506.35041}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 47
\issue 1
\pages 43--72
\crossref{https://doi.org/10.1070/SM1984v047n01ABEH002629}


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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. I. M. Petrushko, “On boundary values in $\mathscr L_p$, $p>1$, of solutions of elliptic equations in domains with a Lyapunov boundary”, Math. USSR-Sb., 48:2 (1984), 565–585  mathnet  crossref  mathscinet  zmath
    2. I. M. Petrushko, “On boundary and initial conditions in $\mathscr L_p$, $p>1$, of solutions of parabolic equations”, Math. USSR-Sb., 53:2 (1986), 489–522  mathnet  crossref  mathscinet  zmath
    3. V. Yu. Shelepov, “On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions”, Math. USSR-Sb., 61:2 (1988), 437–460  mathnet  crossref  mathscinet  zmath  isi
    4. 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
    5. Gushchin A., “On the Dirichlet Problem for the 2nd-Order Elliptic Equation”, 302, no. 5, 1988, 1044–1048  mathscinet  isi
    6. A. K. Gushchin, V. P. Mikhailov, “On the existence of boundary values of solutions of an elliptic equation”, Math. USSR-Sb., 73:1 (1992), 171–194  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. 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
    8. Dumanian V., “Near-Boundary Behavior of the Solution to the Dirichlet Problem for an Elliptic Second-Order Equation”, Dokl. Math., 66:2 (2002), 257–259  mathscinet  isi
    9. 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
    10. 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
    11. Dumanyan V.Zh., “On Boundary Values of Solutions of the Dirichlet Problem for Second Order Elliptic Equation”, J. Contemp. Math. Anal.-Armen. Aca., 45:1 (2010), 26–42  crossref  mathscinet  isi
    12. Dumanyan V.Zh., “O razreshimosti zadachi dirikhle dlya obschego ellipticheskogo uravneniya vtorogo poryadka”, Doklady Akademii nauk, 436:2 (2011), 159–162  elib
    13. Dumanyan V.Zh., “Solvability of the Dirichlet Problem for the General Second-Order Elliptic Equation”, Dokl. Math., 83:1 (2011), 30–33  crossref  mathscinet  zmath  isi
    14. 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
    15. 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
    16. Dumanyan V.Zh., “on Solvability of the Dirichlet Problem With the Boundary Function in l (2) For a Second-Order Elliptic Equation”, J. Contemp. Math. Anal.-Armen. Aca., 50:4 (2015), 153–166  crossref  mathscinet  isi
    17. Petrushko I.M., “On Boundary and Initial Values of Solutions of a Second-Order Parabolic Equation That Degenerate on the Domain Boundary”, Dokl. Math., 96:3 (2017), 568–570  crossref  isi
    18. 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
    19. N. A. Gusev, “On the definitions of boundary values of generalized solutions to an elliptic-type equation”, Proc. Steklov Inst. Math., 301 (2018), 39–43  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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