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Matematicheskie Zametki, 1977, Volume 21, Issue 4, Pages 519–524 (Mi mzm7980)  
The membership of solutions of quasielliptic equations to space $L_p$

V. A. Kondrat'ev, S. D. Èidel'man

M. V. Lomonosov Moscow State University
Full-text PDF (348 kB)
Abstract: It is established that the solutions of a quasielliptic equation, belonging to space $L_1$ with weight equal to a negative power of the distance to the flat part of the boundary, belong to space $L_p$ with some $p>1$. In particular, the positive solutions of uniformly elliptic equations in bounded regions $\Omega$ with a smooth boundary belong to $L_p(\Omega)$ with any $p<n/(n-1)$, where $n$ is the dimension of the space of independent variables.
Received: 24.03.1975
English version:
Mathematical Notes, 1977, Volume 21, Issue 4, Pages 290–293
DOI: https://doi.org/10.1007/BF01787652
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: V. A. Kondrat'ev, S. D. Èidel'man, “The membership of solutions of quasielliptic equations to space $L_p$”, Mat. Zametki, 21:4 (1977), 519–524; Math. Notes, 21:4 (1977), 290–293
Citation in format AMSBIB
\Bibitem{KonEid77}
\by V.~A.~Kondrat'ev, S.~D.~\`Eidel'man
\paper The membership of solutions of quasielliptic equations to space $L_p$
\jour Mat. Zametki
\yr 1977
\vol 21
\issue 4
\pages 519--524
\mathnet{http://mi.mathnet.ru/mzm7980}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=470461}
\zmath{https://zbmath.org/?q=an:0399.35046|0353.35014}
\transl
\jour Math. Notes
\yr 1977
\vol 21
\issue 4
\pages 290--293
\crossref{https://doi.org/10.1007/BF01787652}
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