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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 310, Pages 213–225
(Mi znsl813)
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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
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
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
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https://www.mathnet.ru/eng/znsl813 https://www.mathnet.ru/eng/znsl/v310/p213
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Abstract page: | 180 | Full-text PDF : | 68 | References: | 43 |
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