Change search
ReferencesLink to record
Permanent link

Direct link
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
URN: urn:nbn:se:kth:diva-14758ISI: 000229192400007ScopusID: 2-s2.0-20144376619OAI: diva2:332799
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

Open Access in DiVA

No full text


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
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 20 hits
ReferencesLink to record
Permanent link

Direct link