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Regularity results in free boundary problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of three scientific papers, devoted to the regu-larity theory of free boundary problems. We use iteration arguments to derive the optimal regularity in the optimal switching problem, and to analyse the regularity of the free boundary in the biharmonic obstacle problem and in the double obstacle problem.In Paper A, we study the interior regularity of the solution to the optimal switching problem. We derive the optimal C1,1-regularity of the minimal solution under the assumption that the zero loop set is the closure of its interior.In Paper B, assuming that the solution to the biharmonic obstacle problem with a zero obstacle is suÿciently close-to the one-dimensional solution (xn)3+, we derive the C1,-regularity of the free boundary, under an additional assumption that the noncoincidence set is an NTA-domain.In Paper C we study the two-dimensional double obstacle problem with polynomial obstacles p1 p2, and observe that there is a new type of blow-ups that we call double-cone solutions. We investigate the existence of double-cone solutions depending on the coeÿcients of p1, p2, and show that if the solution to the double obstacle problem with obstacles p1 = −|x|2 and p2 = |x|2 is close to a double-cone solution, then the free boundary is a union of four C1,-graphs, pairwise crossing at the origin.

Place, publisher, year, edition, pages
KTH: KTH Royal Institute of Technology, 2016. , 122 p.
Series
TRITA-MAT-A, 2016-10
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-195178OAI: oai:DiVA.org:kth-195178DiVA: diva2:1044289
Public defence
2016-12-02, D3, Kungl Tekniska Högskolan, Lindstedtsvägen 5, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20161103

Available from: 2016-11-03 Created: 2016-11-02 Last updated: 2016-11-16Bibliographically approved
List of papers
1. Optimal regularity in the optimal switching problem
Open this publication in new window or tab >>Optimal regularity in the optimal switching problem
2016 (English)In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430Article in journal (Refereed) In press
Place, publisher, year, edition, pages
Elsevier, 2016
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-195175 (URN)10.1016/j.anihpc.2015.06.001 (DOI)
Note

QC 20161116

Available from: 2016-11-02 Created: 2016-11-02 Last updated: 2016-11-16Bibliographically approved
2. Regularity of the free boundary in the biharmonic obstacle problem
Open this publication in new window or tab >>Regularity of the free boundary in the biharmonic obstacle problem
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-195176 (URN)
Note

QC 20161116

Available from: 2016-11-02 Created: 2016-11-02 Last updated: 2016-11-16Bibliographically approved
3. Analysis of blow-ups for the double obstacle problem in dimension two
Open this publication in new window or tab >>Analysis of blow-ups for the double obstacle problem in dimension two
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-195177 (URN)
Note

QC 20161116

Available from: 2016-11-02 Created: 2016-11-02 Last updated: 2016-11-16Bibliographically approved

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Citation style
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