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Classification of Singularities in Unstable Free Boundary Problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). (Harmonic analysis and PDE)ORCID iD: 0000-0002-9608-3984
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-177150OAI: oai:DiVA.org:kth-177150DiVA: diva2:871589
Note

QS 201511

Available from: 2015-11-16 Created: 2015-11-16 Last updated: 2016-02-11Bibliographically approved
In thesis
1. Non-linear Free Boundary Problems
Open this publication in new window or tab >>Non-linear Free Boundary Problems
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction and four research papers related to free boundary problems and systems of fully non-linear elliptic equations.

Paper A and Paper B prove optimal regularity of solutions to general elliptic and parabolic free boundary problems, where the operators are fully non-linear and convex. Furthermore, it is proven that the free boundary is continuously differentiable around so called "thick" points, and that the free boundary touches the fixed boundary tangentially in two dimensions.

Paper C analyzes singular points of solutions to perturbations of the unstable obstacle problem, in three dimensions. Blow-up limits are characterized and shown to be unique. The free boundary is proven to lie close to the zero-level set of the corresponding blow-up limit. Finally, the structure of the singular set is analyzed.

Paper D discusses an idea on how existence and uniqueness theorems concerning quasi-monotone fully non-linear elliptic systems can be extended to systems that are not quasi-monotone.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. x, 21 p.
Series
TRITA-MAT-A, 2015:14
Keyword
free boundary, elliptic, fully non-linear
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-178110 (URN)978-91-7595-795-1 (ISBN)
Public defence
2016-01-22, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Note

QC 20151210

Available from: 2015-12-10 Created: 2015-12-07 Last updated: 2015-12-15Bibliographically approved

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Minne, Andreas

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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