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Mathematics of the USSR-Sbornik, 1971, Volume 14, Issue 4, Pages 587–613
DOI: https://doi.org/10.1070/SM1971v014n04ABEH002823
(Mi sm3280)
 

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

On positive solutions of elliptic equations

T. G. Pletneva, S. D. Èidel'man, V. A. Kondrat'ev
References:
Abstract: In this paper the authors study weak solutions of elliptic equations of the form
$$ Pu\equiv\sum_{|k|\leqslant m}(-1)^kD_x^k\bigl(a_k(x)u(x)\bigr)=f(x) $$
in a bounded domain $\Omega$. It is assumed known about these solutions either that they are positive, or that estimates in certain norms hold for their negative parts. It is assumed moreover that an estimate on the $~L_1$-norm of the solution holds on some subdomain $\Omega'\subset\Omega$. Summability of such solutions with a weight function that vanishes at the boundary is established, and with the use of the results of Ya. A. Roitberg integral representations are given in terms of the Green's function for the Dirichlet problem.
Bibliography: 8 titles.
Received: 05.03.1970 and 23.02.1971
Bibliographic databases:
UDC: 517.946
MSC: Primary 35J30; Secondary 35C15, 35D10
Language: English
Original paper language: Russian
Citation: T. G. Pletneva, S. D. Èidel'man, V. A. Kondrat'ev, “On positive solutions of elliptic equations”, Math. USSR-Sb., 14:4 (1971), 587–613
Citation in format AMSBIB
\Bibitem{PleEidKon71}
\by T.~G.~Pletneva, S.~D.~\`Eidel'man, V.~A.~Kondrat'ev
\paper On positive solutions of elliptic equations
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 587--613
\mathnet{http://mi.mathnet.ru//eng/sm3280}
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002823}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=283372}
\zmath{https://zbmath.org/?q=an:0222.35019}
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  • https://doi.org/10.1070/SM1971v014n04ABEH002823
  • https://www.mathnet.ru/eng/sm/v127/i4/p586
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:435
    Russian version PDF:138
    English version PDF:12
    References:89
     
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