Change search
ReferencesLink to record
Permanent link

Direct link
Boundary behaviour for a singular perturbation problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2016 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 138, 176-188 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this paper we study the boundary behaviour of the family of solutions (uε) to singular perturbation problem δuε=βε(uε),(divides)uε(divides)≤1 in B1+=(xn>0)∩((divides)x(divides)<1), where a smooth boundary data f is prescribed on the flat portion of ∂B1+. Here βε((dot operator))=1εβ((dot operator)ε),β∈C0∞(0,1),β≥0,∫01β(t)=M>0 is an approximation of identity. If ∇f(z)=0 whenever f(z)=0 then the level sets ∂(uε>0) approach the fixed boundary in tangential fashion with uniform speed. The methods we employ here use delicate analysis of local solutions, along with elaborated version of the so-called monotonicity formulas and classification of global profiles.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 138, 176-188 p.
Keyword [en]
Free boundary problem, Regularity, Contact points
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-187141DOI: 10.1016/ 000374009200010ScopusID: 2-s2.0-84955297833OAI: diva2:929077
Swedish Research Council

QC 20160517

Available from: 2016-05-17 Created: 2016-05-17 Last updated: 2016-06-01Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Shahgholian, Henrik
By organisation
Mathematics (Div.)
In the same journal
Nonlinear Analysis
Mathematical Analysis

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

Altmetric score

Total: 13 hits
ReferencesLink to record
Permanent link

Direct link