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. ISSN 1097-0312

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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
Volume:	Volume 66
Number:	Number 2
Page Range:	pp. 245-262
Identification Number:	10.1002/cpa.21434
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/49642

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