Optimal regularity for the no-sign obstacle problem
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 1097-0312Full text not available from this repository.
Official URL: http://dx.doi.org/10.1002/cpa.21434
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|
|Official Date:||February 2013|
|Page Range:||pp. 245-262|
|Access rights to Published version:||Restricted or Subscription Access|
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