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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 310, Pages 213–225 (Mi znsl813)  
This article is cited in 3 scientific papers (total in 3 papers)

When does the free boundary enter into corner points of the fixed boundary?

H. Shahgholian

Royal Institute of Technology, Department of Mathematics
Full-text PDF (187 kB) Citations (3)
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Abstract: Our prime goal in this note is to lay the ground for studying free boundaries close to the corner points of a fixed, Lipschitz boundary. Our study is restricted to 2-space dimensions, and to the obstacle problem. Our main result states that the free boundary can not enter into a corner $x^0$ of the fixed boundary, if the (interior) angle is less than $\pi$, provided the boundary datum is zero close to the point $x^0$. For larger angles and other boundary datum the free boundary may enter into corners, as discussed in the text.
Received: 26.05.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 132, Issue 3, Pages 371–377
DOI: https://doi.org/10.1007/s10958-005-0504-5
Bibliographic databases:
UDC: 517
Language: English
Citation: H. Shahgholian, “When does the free boundary enter into corner points of the fixed boundary?”, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Zap. Nauchn. Sem. POMI, 310, POMI, St. Petersburg, 2004, 213–225; J. Math. Sci. (N. Y.), 132:3 (2006), 371–377
Citation in format AMSBIB
\Bibitem{Sha04}
\by H.~Shahgholian
\paper When does the free boundary enter into corner points of the fixed boundary?
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~35
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 310
\pages 213--225
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl813}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2120191}
\zmath{https://zbmath.org/?q=an:1082.35171}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 132
\issue 3
\pages 371--377
\crossref{https://doi.org/10.1007/s10958-005-0504-5}
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  • https://www.mathnet.ru/eng/znsl/v310/p213
    • 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
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