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Optimal regularity for the obstacle problem for the p-Laplacian
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2015 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 6, 2167-2179 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we discuss the obstacle problem for the p-Laplace operator. We prove optimal growth results for the solution. Of particular interest is the point-wise regularity of the solution at free boundary points. The most surprising result we prove is the one for the p-obstacle problem: Find the smallest u such thatdiv(|∇u|p-2∇u)≤0,u≥ϕ,in B1, with ϕ∈C1,1(B1) and given boundary datum on ∂B1. We prove that the solution is uniformly C1,1 at free boundary points. Similar results are obtained in the case of an inhomogeneity belonging to L∞. When applied to the corresponding parabolic problem, these results imply that any solution which is Lipschitz in time is C1,1p-1 in the spatial variables.

Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 259, no 6, 2167-2179 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-170288DOI: 10.1016/j.jde.2015.03.019ISI: 000368466500003Scopus ID: 2-s2.0-84930540839OAI: oai:DiVA.org:kth-170288DiVA: diva2:833656
Funder
Swedish Research Council, 2012-3124
Note

QC 20150630. QC 20160216

Available from: 2015-06-30 Created: 2015-06-29 Last updated: 2017-12-04Bibliographically approved

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Lindgren, ErikShahgholian, Henrik

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