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On the penalized obstacle problem in the unit half ball
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-4309-9242
2010 (English)In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, no 9, 1-12 p.Article in journal (Refereed) Published
Abstract [en]

We study the penalized obstacle problem in the unit half ball,i.e. an approximation of the obstacle problem in the unit half ball. The mainresult states that when the approximation parameter is small enough and whencertain level sets are sufficiently close to the hyperplane {x1 = 0}, then theselevel sets are uniformly C1 regular graphs. As a by-product, we also recoversome regularity of the free boundary for the limiting problem, i.e., for theobstacle problem.

Place, publisher, year, edition, pages
2010. no 9, 1-12 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-10335OAI: oai:DiVA.org:kth-10335DiVA: diva2:214788
Note
QC 20100728Available from: 2009-05-06 Created: 2009-05-06 Last updated: 2017-12-13Bibliographically approved
In thesis
1. Regularity properties of two-phase free boundary problems
Open this publication in new window or tab >>Regularity properties of two-phase free boundary problems
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers which are all related to the regularity properties of free boundary problems. The problems considered have in common that they have some sort of two-phase behaviour.In papers I-III we study the interior regularity of different two-phase free boundary problems. Paper I is mainly concerned with the regularity properties of the free boundary, while in papers II and III we devote our study to the regularity of the function, but as a by-product we obtain some partial regularity of the free boundary.The problem considered in paper IV has a somewhat different nature. Here we are interested in certain approximations of the obstacle problem. Two major differences are that we study regularity properties close to the fixed boundary and that the problem converges to a one-phase free boundary problem.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. viii, 36 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 09:07
Keyword
Mathematics
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-10336 (URN)978-91-7415-288-3 (ISBN)
Public defence
2009-06-05, F3, Lindstedtsvägen 26, KTH, 14:00 (English)
Opponent
Supervisors
Note
QC 20100728Available from: 2009-05-26 Created: 2009-05-06 Last updated: 2010-07-28Bibliographically approved

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Lindgren, Erik

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