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Aleksandrov and Kelvin reflection and the regularity of free boundaries
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2007 (English)In: Free Boundary Problems: Theory and Applications / [ed] Figueiredo, IN; Rodrigues, JF; Santos, L, 2007, Vol. 154, 391-401 p.Conference paper, Published paper (Refereed)
Abstract [en]

The first part of this paper is an announcement of a result to appear. We apply the Aleksandrov reflection to obtain regularity and stability of the free boundaries in the two-dimensional problem Delta u = lambda+/2 chi{u > 0} - lambda-/2 chi{u < 0}, where lambda(+) > 0 and lambda(-) > 0. In the second part we show that the Kelvin reflection can be used in a similar way to obtain regularity of the classical obstacle problem Delta u = chi{u > 0} in higher dimensions.

Place, publisher, year, edition, pages
2007. Vol. 154, 391-401 p.
Series
International Series Of Numerical Mathematics, ISSN 0373-3149 ; 154
Keyword [en]
free boundary, singular point, branch point, obstacle problem, regularity, Kelvin transform, global solution, blow-up, monotonicity formula
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-39130DOI: 10.1007/978-3-7643-7719-9_38ISI: 000244480600038ISBN: 978-3-7643-7718-2 (print)OAI: oai:DiVA.org:kth-39130DiVA: diva2:439787
Conference
Free Boundary Problems Conference (FBP2005) Location: Univ Coimbra, Coimbra, Portugal Date: JUN 07-12, 2005
Available from: 2011-09-09 Created: 2011-09-08 Last updated: 2011-09-09Bibliographically approved

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Shahgholian, Henrik

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