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Mat. Sb. (N.S.), 1972, Volume 89(131), Number 1(9), Pages 16–45 (Mi msb3215)  

This article is cited in 1 scientific paper (total in 1 paper)

Positive solutions of linear quasielliptic evolution equations

V. A. Kondrat'ev, T. G. Pletneva, S. D. Èidel'man


Abstract: We study a new class of elliptic equations whose characteristic surfaces are hyperplanes $t=\mathrm{const}$. We establish integrability of positive solutions of such equations with power weights in regions adjoining characteristic hyperplanes and in cylinders with generators parallel to the time axis. Information is obtained on the behavior of such solutions in unbounded regions. Examples which illustrate the accuracy of the results are mentioned.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 18:1, 15–44

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J30, 35B45; Secondary 35J70, 35B05
Received: 09.06.1971

Citation: V. A. Kondrat'ev, T. G. Pletneva, S. D. Èidel'man, “Positive solutions of linear quasielliptic evolution equations”, Mat. Sb. (N.S.), 89(131):1(9) (1972), 16–45; Math. USSR-Sb., 18:1 (1972), 15–44

Citation in format AMSBIB
\Bibitem{KonPleEid72}
\by V.~A.~Kondrat'ev, T.~G.~Pletneva, S.~D.~\`Eidel'man
\paper Positive solutions of linear quasielliptic evolution equations
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 89(131)
\issue 1(9)
\pages 16--45
\mathnet{http://mi.mathnet.ru/msb3215}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=310424}
\zmath{https://zbmath.org/?q=an:0258.35014}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 1
\pages 15--44
\crossref{https://doi.org/10.1070/SM1972v018n01ABEH001609}


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    This publication is cited in the following articles:
    1. V. A. Kondrat'ev, S. D. Èidel'man, “On the summability of positive solutions of partial differential equations of arbitrary order in a neighborhood of a characteristic manifold”, Math. USSR-Sb., 28:4 (1976), 521–531  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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