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Mat. Sb. (N.S.), 1976, Volume 99(141), Number 4, Pages 582–593 (Mi msb2776)  

On the summability of positive solutions of partial differential equations of arbitrary order in a neighborhood of a characteristic manifold

V. A. Kondrat'ev, S. D. Èidel'man


Abstract: A nonnegative solution of the equation $\sum_{|\alpha|\leqslant m}a_\alpha(x)D^\alpha u=0$ is considered in an arbitrary domain $G$ with smooth boundary $\Gamma$.
The surface $\Gamma$ can contain a characteristic manifold $\Gamma_0$. Conditions on $\Gamma_0$ are obtained ensuring that $\int_Gu dx$ is always finite. These conditions turn out to be best possible.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 28:4, 521–531

Bibliographic databases:

UDC: 517.946
MSC: Primary 35B99, 35G99; Secondary 35K05
Received: 06.02.1975

Citation: 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”, Mat. Sb. (N.S.), 99(141):4 (1976), 582–593; Math. USSR-Sb., 28:4 (1976), 521–531

Citation in format AMSBIB
\Bibitem{KonEid76}
\by V.~A.~Kondrat'ev, S.~D.~\`Eidel'man
\paper On the summability of positive solutions of partial differential equations of arbitrary order in a~neighborhood of a~characteristic manifold
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 4
\pages 582--593
\mathnet{http://mi.mathnet.ru/msb2776}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=422841}
\zmath{https://zbmath.org/?q=an:0341.35023}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 4
\pages 521--531
\crossref{https://doi.org/10.1070/SM1976v028n04ABEH001667}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EQ33200006}


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