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Matematicheskie Zametki, 1971, Volume 9, Issue 1, Pages 89–92 (Mi mzm9647)  
This article is cited in 22 scientific papers (total in 22 papers)

Solution of Dirichlet's problem for the equation $\Delta u=-1$ in a convex region

L. G. Makar-Limanov

M. V. Lomonosov Moscow State University
Full-text PDF (303 kB) Citations (22)
Abstract: Let $u$ be a solution of the following boundary-value problem: $u|_\Gamma=0$, where $\Gamma$ is a closed convex curve and $\Delta u=-1$ in the region $D$ bounded by $\Gamma$. Then $u$ has only one local maximum, and all its level curves are convex.
Received: 06.10.1969
English version:
Mathematical Notes, 1971, Volume 9, Issue 1, Pages 52–53
DOI: https://doi.org/10.1007/BF01405053
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: L. G. Makar-Limanov, “Solution of Dirichlet's problem for the equation $\Delta u=-1$ in a convex region”, Mat. Zametki, 9:1 (1971), 89–92; Math. Notes, 9:1 (1971), 52–53
Citation in format AMSBIB
\Bibitem{Mak71}
\by L.~G.~Makar-Limanov
\paper Solution of Dirichlet's problem for the equation $\Delta u=-1$ in a convex region
\jour Mat. Zametki
\yr 1971
\vol 9
\issue 1
\pages 89--92
\mathnet{http://mi.mathnet.ru/mzm9647}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=279321}
\zmath{https://zbmath.org/?q=an:0222.31004|0206.40405}
\transl
\jour Math. Notes
\yr 1971
\vol 9
\issue 1
\pages 52--53
\crossref{https://doi.org/10.1007/BF01405053}
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    • This publication is cited in the following 22 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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