Digitala Vetenskapliga Arkivet

Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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
  • text
  • asciidoc
  • rtf
Viscosity Solutions of Balanced Quasi-Monotone Fully Nonlinear Weakly Coupled Systems
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-177149OAI: oai:DiVA.org:kth-177149DiVA, id: diva2:871588
Note

QP 201511

Available from: 2015-11-16 Created: 2015-11-16 Last updated: 2022-06-23Bibliographically 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. p. x, 21
Series
TRITA-MAT-A ; 2015:14
Keywords
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: 2022-06-23Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

http://arxiv.org/abs/1403.7106

Search in DiVA

By author/editor
Minne, Andreas
By organisation
Mathematics (Div.)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 1457 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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
  • text
  • asciidoc
  • rtf