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
Non-convexity of level sets in convex rings for semilinear elliptic problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2005 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, Vol. 54, no 2, 465-471 p.Article in journal (Refereed) Published
Abstract [en]

We show that there is a convex ring R = Omega(-) \ Q(+) C R-2 in which there exists a solution u to a semilinear partial differential equation Delta u = f(u), u = -1 on partial derivative Omega(-), u = 1 on partial derivative Omega(+), with level sets, not all convex. Moreover, every bounded solution u has at least one non-convex level set. In our construction, the nonlinearity f, is non-positive, and smooth.

Place, publisher, year, edition, pages
2005. Vol. 54, no 2, 465-471 p.
Keyword [en]
non-convexity, level set, semilinear elliptic equation, convex ring, singular perturbation problem, free-boundary problems, regular solutions, plasma physics, fluid-dynamics, equations, nonlinearities, existence, limit
Identifiers
URN: urn:nbn:se:kth:diva-14758ISI: 000229192400007Scopus ID: 2-s2.0-20144376619OAI: oai:DiVA.org:kth-14758DiVA: diva2:332799
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

Open Access in DiVA

No full text

Scopus

Authority records BETA

Shahgholian, Henrik

Search in DiVA

By author/editor
Shahgholian, Henrik
By organisation
Mathematics (Div.)
In the same journal
Indiana University Mathematics Journal

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 26 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