Change search
CiteExportLink to record
Permanent link

Direct link
Cite
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
  • text
  • asciidoc
  • rtf
Regularity of the free boundary in a two-phase semilinear problem in two dimensions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-4309-9242
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2008 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 57, no 7, 3397-3418 p.Article in journal (Refereed) Published
Abstract [en]

We study minimizers of the energy functional ∫D (|∇u|2 + 2(λ+(u+)p + λ-(u-)p)) dx for p ∈ (0, 1) without any sign restriction on the function u. The main result states that in dimension two the free boundaries Γ+ = ∂{u > 0} ∩ D and Γ- = ∂{u < 0} n D are C1 regular.

Place, publisher, year, edition, pages
2008. Vol. 57, no 7, 3397-3418 p.
Keyword [en]
Alexandrov reflection-comparison; Monotonicity formula; Regularity of the free boundary; Semilinear equation
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-10332DOI: 10.1512/iumj.2008.57.3433ISI: 000263576400014Scopus ID: 2-s2.0-62649101823OAI: oai:DiVA.org:kth-10332DiVA: diva2:214777
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

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Lindgren, Erik

Search in DiVA

By author/editor
Lindgren, ErikPetrosyan, Arshak
By organisation
Mathematics (Dept.)
In the same journal
Indiana University Mathematics Journal
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 34 hits
CiteExportLink to record
Permanent link

Direct link
Cite
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
  • text
  • asciidoc
  • rtf