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Matematicheskie Zametki, 1993, Volume 53, Issue 1, Pages 68–82 (Mi mzm3921)  

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

Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form

F. I. Mamedov

Azerbaijan polytechnic Institute named after Ch. Il'drym
Abstract: We prove estimates in $C(D)$ and $L_p(D)$ and in Orlicz norms of solutions of the following linear and quasilinear equations:
$$ \sum_{i,k=1}^n\frac\partial{\partial x_i}\biggl(a_{ik}(x)\frac{\partial u}{\partial x_k}\biggr)+\sum_{i=1}^n\frac\partial{\partial x_i}(b_i(x)u)+c(x)u=\sum_{i=1}^n\frac{\partial f^i}{\partial x_i} $$
and
$$ \sum_{i=1}^n\frac\partial{\partial x_i}\bigl(a_i(x,u,\nabla u)\bigr)+h(x,u)=\sum_{i=1}^n\frac{\partial f^i}{\partial x_i}, $$
depending on the membership of the functions $c(x)$, $b_i(x)$ and $f^i(x)$ in various spaces $L_p(D)$. We write out explicitly the constants in the estimates obtained.
Received: 12.11.1990
English version:
Mathematical Notes, 1993, Volume 53, Issue 1, Pages 50–58
DOI: https://doi.org/10.1007/BF01208522
Bibliographic databases:
UDC: 517.944
Language: Russian
Citation: F. I. Mamedov, “Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form”, Mat. Zametki, 53:1 (1993), 68–82; Math. Notes, 53:1 (1993), 50–58
Citation in format AMSBIB
\Bibitem{Mam93}
\by F.~I.~Mamedov
\paper Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form
\jour Mat. Zametki
\yr 1993
\vol 53
\issue 1
\pages 68--82
\mathnet{http://mi.mathnet.ru/mzm3921}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1215160}
\zmath{https://zbmath.org/?q=an:0838.35027}
\transl
\jour Math. Notes
\yr 1993
\vol 53
\issue 1
\pages 50--58
\crossref{https://doi.org/10.1007/BF01208522}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993MY10400007}
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  • https://www.mathnet.ru/eng/mzm/v53/i1/p68
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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