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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 221, Pages 5–19 (Mi znsl4292)  
This article is cited in 7 scientific papers (total in 8 papers)

On the behavior of free boundaries near the boundary of the domain

D. E. Apushkinskayaa, N. N. Uraltsevab

a St. Petersburg State University of Architecture and Civil Engineering
b Saint-Petersburg State University
Full-text PDF (550 kB) Citations (8)
Abstract: Let $u$ be a solution of the obstacle problem $u\ge0$, $-\Delta u+f\ge0$, $u(-\Delta u+f)=0$ in a domain $\Omega\subset\mathbb R^n$. In this paper, the behaviour of the free boundary in a neighborhood of $\partial\Omega$ is studied. It is proved that under some conditions the free boundary touches $\partial\Omega$ at contact points. Bibliography: 4 titles.
Received: 20.04.1995
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 87, Issue 2, Pages 3267–3276
DOI: https://doi.org/10.1007/BF02355579
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: D. E. Apushkinskaya, N. N. Uraltseva, “On the behavior of free boundaries near the boundary of the domain”, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Zap. Nauchn. Sem. POMI, 221, POMI, St. Petersburg, 1995, 5–19; J. Math. Sci. (New York), 87:2 (1997), 3267–3276
Citation in format AMSBIB
\Bibitem{ApuUra95}
\by D.~E.~Apushkinskaya, N.~N.~Uraltseva
\paper On the behavior of free boundaries near the boundary of the domain
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 221
\pages 5--19
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4292}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1359745}
\zmath{https://zbmath.org/?q=an:0927.35135|0888.35141}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 2
\pages 3267--3276
\crossref{https://doi.org/10.1007/BF02355579}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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