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Mat. Sb. (N.S.), 1970, Volume 82(124), Number 4(8), Pages 551–573 (Mi msb3467)  

This article is cited in 2 scientific papers (total in 2 papers)

On the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations

V. I. Feigin


Abstract: We investigate the question of smoothness for solutions of the first and second boundary problems for a class of degenerate equations (including, in particular, a parabolic equation) in domains with boundaries containing characteristic points.
In the case of tangency of higher degree of the boundary with a characteristic plane conditions are given which guarantee that the solution belongs to the space $H_p$.
Bibliography: 9 titles.

Full text: PDF file (1759 kB)
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English version:
Mathematics of the USSR-Sbornik, 1970, 11:4, 507–528

Bibliographic databases:

UDC: 517.946.9
MSC: 35B65, 35K20, 35J25, 35J70, 35B45, 35D05
Received: 10.06.1969 and 27.01.1970

Citation: V. I. Feigin, “On the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations”, Mat. Sb. (N.S.), 82(124):4(8) (1970), 551–573; Math. USSR-Sb., 11:4 (1970), 507–528

Citation in format AMSBIB
\Bibitem{Fei70}
\by V.~I.~Feigin
\paper On~the smoothness of the solutions of boundary value problems for parabolic and degenerate elliptic equations
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 82(124)
\issue 4(8)
\pages 551--573
\mathnet{http://mi.mathnet.ru/msb3467}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=274941}
\zmath{https://zbmath.org/?q=an:0233.35042}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 4
\pages 507--528
\crossref{https://doi.org/10.1070/SM1970v011n04ABEH001303}


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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. V. N. Aref'ev, L. A. Bagirov, “Asymptotic behavior of solutions to the Dirichlet problem for parabolic equations in domains with singularities”, Math. Notes, 59:1 (1996), 10–17  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. N. Aref'ev, L. A. Bagirov, “Solutions of the heat equation in domains with singularities”, Math. Notes, 64:2 (1998), 139–153  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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