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Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2014 (English)In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, Vol. 101, no 2, 119-151 p.Article in journal (Other academic) Published
Abstract [en]

In this paper we prove, by showing that solutions have exactly the same degree of regularity as the obstacle, optimal regularity results for obstacle problems involving evolutionary p-Laplace type operators. A main ingredient, of independent interest, is a new intrinsic interpolative geometry allowing for optimal linearization principles via blow-up analysis at contact points. This also opens the way to the proof of a removability theorem for solutions to evolutionary p-Laplace type equations. A basic feature of the paper is that no differentiability in time is assumed on the obstacle; this is in line with the corresponding linear results.

Place, publisher, year, edition, pages
2014. Vol. 101, no 2, 119-151 p.
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URN: urn:nbn:se:uu:diva-184530DOI: 10.1016/j.matpur.2013.03.004ISI: 000331666000001OAI: diva2:566040
Available from: 2012-11-09 Created: 2012-11-08 Last updated: 2014-03-25Bibliographically approved

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Nyström, Kaj
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