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Analysis of blow-ups for the double obstacle problem in dimension two
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 21, no 2, p. 131-167Article in journal (Refereed) Published
Abstract [en]

In this article we study a normalised double obstacle problem with polynomial obstacles p(1)(x) <= p(2)(x), where the equality holds iff x = 0. In dimension two we give a complete classification of blow-up solutions. In particular, we see that there exists a new type of blow-ups, which we call double-cone solutions, since the coincidence sets {u = p(1)} and {u = p(2)} are cones with a common vertex. Furthermore, we show that if the solution to the double obstacle problem has a double-cone blow-up limit at the origin, then the blow-up is unique, and locally the free boundary consists of four C-1,C-gamma-curves, meeting at the origin.

Place, publisher, year, edition, pages
European Mathematical Society Publishing House, 2019. Vol. 21, no 2, p. 131-167
Keywords [en]
Obstacle problem, free boundary, global solution, regularity theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-255780DOI: 10.4171/IFB/419ISI: 000476649500001Scopus ID: 2-s2.0-85070192277OAI: oai:DiVA.org:kth-255780DiVA, id: diva2:1341612
Note

QC 20190809

Available from: 2019-08-09 Created: 2019-08-09 Last updated: 2019-10-04Bibliographically approved

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