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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. ISSN 1097-0312
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Official URL: http://dx.doi.org/10.1002/cpa.21434
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 |
| 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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