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});});

Boundary Regularity and Compactness for Overdetermined ProblemsPrimeFaces.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}); 2003 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, Vol. 2, no 4, 787-802 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2003. Vol. 2, no 4, 787-802 p.
##### Identifiers

URN: urn:nbn:se:kth:diva-23237ISI: 000207016700006OAI: oai:DiVA.org:kth-23237DiVA: diva2:341935
#####

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});
##### Note

QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

Let D be either the unit ball B-1(0) or the half ball B-1(+)(0), let f be a strictly positive and continuous function, and let u and Omega subset of D solve the following overdetermined problem: Delta u (x) = chi(Omega) (x) f (x) in D, 0 is an element of partial derivative Omega, u = vertical bar del u vertical bar = 0 in Omega(c), where chi(Omega) denotes the characteristic function of Omega, Omega(c) denotes the set D\Omega, and the equation is satisfied in the sense of distributions. When D = B-1(+)(0), then we impose in addition that u(x) 0 {(x', x(n))vertical bar x(n) = 0} We show that a fairly mild thickness assumption on Omega(c) will ensure enough compactness on it to give us "blow-up" limits, and we show how this compactness leads to regularity of partial derivative Omega. In the case where f is positive and Lipschitz, the methods developed in Caffarelli, Karp, and Shahgholian (2000) lead to regularity of partial derivative Omega under a weaker thickness assumption.

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});});