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Convexity Of The Free Boundary For An Exterior Free Boundary Problem Involving The Perimeter
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2013 (English)In: Communications on Pure and Applied Analysis, ISSN 1534-0392, Vol. 12, no 3, 1431-1443 p.Article in journal (Refereed) Published
Abstract [en]

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = integral(BR) vertical bar del v vertical bar(p)dx + Per({v > 0}), 1 < p < infinity, over the set {v epsilon W-0(1,P)(BR)vertical bar v 1 on K subset of BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

Place, publisher, year, edition, pages
2013. Vol. 12, no 3, 1431-1443 p.
Keyword [en]
Free boundary problems, mean curvature
National Category
URN: urn:nbn:se:kth:diva-106109DOI: 10.3934/cpaa.2013.12.1431ISI: 000310647400019ScopusID: 2-s2.0-84873316680OAI: diva2:573608

QC 20121203

Available from: 2012-12-03 Created: 2012-11-29 Last updated: 2012-12-03Bibliographically approved

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Shahgholian, Henrik
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