References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On the singularities of a free boundary through Fourier expansionPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 187, no 3, 535-587 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012. Vol. 187, no 3, 535-587 p.
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-82114DOI: 10.1007/s00222-011-0336-5ISI: 000302695800002ScopusID: 2-s2.0-84857796756OAI: oai:DiVA.org:kth-82114DiVA: diva2:497943
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Funder

Swedish Research Council
##### Note

QC 20120509Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2012-05-09Bibliographically approved

In this paper we are concerned with singular points of solutions to the unstable free boundary problem Delta u = -chi({u>0}) in B-1. The problem arises in applications such as solid combustion, composite membranes, climatology and fluid dynamics. It is known that solutions to the above problem may exhibit singularities-that is points at which the second derivatives of the solution are unbounded-as well as degenerate points. This causes breakdown of by-now classical techniques. Here we introduce new ideas based on Fourier expansion of the non-linearity chi({u>0}). The method turns out to have enough momentum to accomplish a complete description of the structure of the singular set in R-3. A surprising fact in R-3 is that although u(rx)/sup(B1) vertical bar u(rx)vertical bar can converge at singularities to each of the harmonic polynomials xy, x(2) + y(2)/2 - z(2) and z(2) - x(2) + y(2)/2, it may not converge to any of the non-axially-symmetric harmonic polynomials alpha((1 + delta)x(2) + (1 - delta)y(2) - 2z(2)) with delta not equal 1/2. We also prove the existence of stable singularities in R-3.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});