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Optimal regularity for the no-sign obstacle problem

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Andersson, John, Lindgren, E. and Shahgholian, H. (2013) Optimal regularity for the no-sign obstacle problem. Communications in Pure and Applied Mathematics, Volume 66 (Number 2). pp. 245-262. doi:10.1002/cpa.21434

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Official URL: http://dx.doi.org/10.1002/cpa.21434

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Abstract

In this paper we prove the optimal -regularity for a general obstacle-type problem

under the assumption that is , where N is the Newtonian potential. This is the weakest assumption for which one can hope to get -regularity. As a by-product of the -regularity we are able to prove that, under a standard thickness assumption on the zero set close to a free boundary point , the free boundary is locally a -graph close to 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. © 2012 Wiley Periodicals, Inc.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Communications in Pure and Applied Mathematics
Publisher: Wiley-Blackwell Publishing, Inc
ISSN: 1097-0312
Official Date: February 2013
Dates:
DateEvent
February 2013Published
Volume: Volume 66
Number: Number 2
Page Range: pp. 245-262
DOI: 10.1002/cpa.21434
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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