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Optimal Regularity for the No-Sign Obstacle Problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2013 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 66, no 2, 245-262 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we prove the optimal C-1,C-1(B-1/2)-regularity for a general obstacle-type problem Delta u = f chi({u not equal 0}) in B-1, under the assumption that f * N is C-1,C-1(B-1), where N is the Newtonian potential. This is the weakest assumption for which one can hope to get C-1,C-1-regularity. As a by-product of the C-1,C-1-regularity we are able to prove that, under a standard thickness assumption on the zero set close to a free boundary point x(0), the free boundary is locally a C-1-graph close to x(0) provided f is Dini. This completely settles the question of the optimal regularity of this problem, which has been the focus of much attention during the last two decades.

Place, publisher, year, edition, pages
2013. Vol. 66, no 2, 245-262 p.
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URN: urn:nbn:se:kth:diva-109167DOI: 10.1002/cpa.21434ISI: 000311611800004ScopusID: 2-s2.0-84870356228OAI: diva2:580366
Swedish Research Council

QC 20121221

Available from: 2012-12-21 Created: 2012-12-21 Last updated: 2012-12-21Bibliographically approved

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Shahgholian, Henrik
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