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Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2014 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 1, 21-42 p.Article in journal (Refereed) Published
##### Abstract [en]

We study minimizers of the functional where B_{1}^{{\mathchoice {\raise .17ex\hbox {\scriptstyle +}} {\raise .17ex\hbox {\scriptstyle +}} {\raise .1ex\hbox {\scriptscriptstyle +}} {\scriptscriptstyle +}}}=\{x\in B_{1}: x_{1}>0\} , u=0 on {xB 1:x 1=0}, \lambda^{{\mathchoice {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .17ex\hbox {\scriptstyle \pm }} {\raise .1ex\hbox {\scriptscriptstyle \pm }} {\scriptscriptstyle \pm }}} are two positive constants and 0<p<1. In two dimensions, we prove that the free boundary is a uniform C 1 graph up to the flat part of the fixed boundary and also that two-phase points cannot occur on this part of the fixed boundary. Here, the free boundary refers to the union of the boundaries of the sets {xu(x)>0}.

##### Place, publisher, year, edition, pages
2014. Vol. 52, no 1, 21-42 p.
##### National Category
Mathematical Analysis
##### Identifiers
ISI: 000332797200003OAI: oai:DiVA.org:uu-170218DiVA: diva2:508616
Available from: 2012-03-13 Created: 2012-03-09 Last updated: 2017-12-07Bibliographically approved

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Cite
Citation style
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