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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 2(6), Pages 241–259 (Mi msb1739)  

This article is cited in 3 scientific papers (total in 3 papers)

On boundary values of solutions of elliptic equations degenerating on the boundary

I. M. Petrushko


Abstract: Necessary and sufficient conditions are established for the existence, on the domain's boundary, of a limit in $\mathscr L_p$, $p>1$, of solutions of second order elliptic equations having Tricomi type degeneracy on the boundary.
Solvability of the Dirichlet problem for such an equation in spaces of type $W^1_{p,\mathrm{loc}}$ is proved.
Bibliography: 9 titles.

Full text: PDF file (784 kB)
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English version:
Mathematics of the USSR-Sbornik, 1989, 64:1, 243–262

Bibliographic databases:

UDC: 517.956
MSC: 35J70
Received: 30.06.1987

Citation: I. M. Petrushko, “On boundary values of solutions of elliptic equations degenerating on the boundary”, Mat. Sb. (N.S.), 136(178):2(6) (1988), 241–259; Math. USSR-Sb., 64:1 (1989), 243–262

Citation in format AMSBIB
\Bibitem{Pet88}
\by I.~M.~Petrushko
\paper On boundary values of solutions of elliptic equations degenerating on the boundary
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 2(6)
\pages 241--259
\mathnet{http://mi.mathnet.ru/msb1739}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=954927}
\zmath{https://zbmath.org/?q=an:0683.35034}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 243--262
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003305}


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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. Petrushko I., “On Boundary-Values of Solutions of Parabolic Equations Degenerating on Domains Boundary”, 316, no. 3, 1991, 550–552  mathscinet  isi
    2. I. M. Petrushko, “Existence of boundary values for solutions of degenerate elliptic equations”, Sb. Math., 190:7 (1999), 973–1004  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Petrushko I.M., Kapitsyna T.V., “O pervoi smeshannoi zadache v lp, r > 1, dlya vyrozhdayuschikhsya parabolicheskikh uravnenii”, Vestnik moskovskogo energeticheskogo instituta, 2011, no. 6, 143–154  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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