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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
Identifiers
URN: urn:nbn:se:kth:diva-187141DOI: 10.1016/j.na.2015.12.024ISI: 000374009200010ScopusID: 2-s2.0-84955297833OAI: oai:DiVA.org:kth-187141DiVA: diva2:929077
Funder
Swedish Research Council
Note

QC 20160517

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

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Shahgholian, Henrik
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Mathematics (Div.)
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