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The regularity theory for the double obstacle problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2019 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 58, no 3, article id 104Article in journal (Refereed) Published
Abstract [en]

In this paper, we prove a local C1-regularity of the free boundary for the (hybrid) double obstacle problem with an upper obstacle , Delta u< =f chi Omega(u)boolean AND{u<psi}+Delta psi chi Omega(u boolean AND){u=psi},u <=psi in B1, where Omega (u) = B-1\({u = 0} boolean AND {del u = 0})under a thickness assumption for u and . The novelty of the paper is the study of points where two obstacles meet, here it refers to free boundary points where =0. Our result is new, with a non-straightforward approach, as the analysis seems to require several subtle manoeuvres in finding the right conditions and methodology. A key point of difficulty lies in the classification of global solutions. This is due to the complex structure of global solutions for the double obstacle problem, and even more complex for the hybrid problem in this paper.

Place, publisher, year, edition, pages
2019. Vol. 58, no 3, article id 104
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-252963DOI: 10.1007/s00526-019-1543-yISI: 000468929600002Scopus ID: 2-s2.0-85067646532OAI: oai:DiVA.org:kth-252963DiVA, id: diva2:1340239
Note

QC 20190802

Available from: 2019-08-02 Created: 2019-08-02 Last updated: 2019-08-02Bibliographically approved

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Shahgholian, Henrik

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