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When does the free boundary enter into corner points of the fixed boundary?
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
2006 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 132, no 3, 371-377 p.Article in journal (Refereed) Published
Abstract [en]

Our prime goal in this note is to lay the ground for studying free boundaries close to the corner points of a fixed Lipschitz continuous boundary. Our study is restricted to 2-space dimensions and to the obstacle problem. Our main result states that the free boundary cannot enter a corner x0 of the fixed boundary if the (interior) angle is less than π, provided that the boundary datum is zero near to the point x0. For larger angles and other boundary data, the free boundary may enter into corners, as discussed in the text. Bibliography: 10 titles.

Place, publisher, year, edition, pages
2006. Vol. 132, no 3, 371-377 p.
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URN: urn:nbn:se:kth:diva-82043DOI: 10.1007/s10958-005-0504-5ScopusID: 2-s2.0-29144480445OAI: diva2:497861

QC 20120227

Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2012-10-10Bibliographically approved

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Shahgholian, Henrik
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