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Optimal regularity for the parabolic no-sign obstacle type problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-4309-9242
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2013 (English)In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, no 4, 477-499 p.Article in journal (Refereed) Published
Abstract [en]

We study the parabolic free boundary problem of obstacle type Delta u - partial derivative u/partial derivative t = f chi({u not equal 0}). Under the condition that f = H nu for some function nu with bounded second order spatial derivatives and bounded first order time derivative, we establish the same regularity for the solution u. Both the regularity and the assumptions are optimal. Using this result and assuming that f is Dini continuous, we prove that the free boundary is, near so called low energy points, a C-1 graph. Our result completes the theory for this type of problems for the heat operator.

Place, publisher, year, edition, pages
2013. Vol. 15, no 4, 477-499 p.
Keyword [en]
Free boundary problem, parabolic equation, regularity, Dini condition
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-141375DOI: 10.4171/IFB/311ISI: 000329995600004Scopus ID: 2-s2.0-84893712628OAI: oai:DiVA.org:kth-141375DiVA: diva2:696501
Note

QC 20140214

Available from: 2014-02-14 Created: 2014-02-14 Last updated: 2017-12-06Bibliographically approved

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Lindgren, ErikShahgholian, Henrik

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