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A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2014 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 213, no 1, 269-286 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the fully nonlinear free boundary problem {F(D(2)u) = 1 almost everywhere in B-1 boolean AND Omega vertical bar D(2)u vertical bar <= K almost everywhhere in B-1\Omega, where K > 0, and Omega is an unknown open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W (2,n) solutions are locally C (1,1) inside B (1). Under the extra condition that and a uniform thickness assumption on the coincidence set {D u = 0}, we also show local regularity for the free boundary partial derivative Omega boolean AND B-1.

Place, publisher, year, edition, pages
2014. Vol. 213, no 1, 269-286 p.
Keyword [en]
Viscosity Solutions, Regularity
National Category
URN: urn:nbn:se:kth:diva-145794DOI: 10.1007/s00205-014-0734-0ISI: 000335158200007ScopusID: 2-s2.0-84899977135OAI: diva2:721097
Swedish Research Council

QC 20140603

Available from: 2014-06-03 Created: 2014-06-02 Last updated: 2014-06-03Bibliographically approved

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Shahgholian, Henrik
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