CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt144",{id:"formSmash:upper:j_idt144",widgetVar:"widget_formSmash_upper_j_idt144",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt145_j_idt147",{id:"formSmash:upper:j_idt145:j_idt147",widgetVar:"widget_formSmash_upper_j_idt145_j_idt147",target:"formSmash:upper:j_idt145:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Monotonicity formulas and applications in free boundary 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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Stockholm: KTH , 2010. , p. 37
##### Keyword [en]

Partial differential equations, PDE, Free boundary problems, Monotonicity formulas
##### National Category

Mathematical Analysis
##### Identifiers

URN: urn:nbn:se:kth:diva-12405ISBN: 978-91-7415-595-2 (print)OAI: oai:DiVA.org:kth-12405DiVA, id: diva2:310874
##### Public defence

2010-05-07, F3, Lindstedtsvägen 26, Stockholm, 13:00 (English)
##### Opponent

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

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt473",{id:"formSmash:j_idt473",widgetVar:"widget_formSmash_j_idt473",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt479",{id:"formSmash:j_idt479",widgetVar:"widget_formSmash_j_idt479",multiple:true});
##### Note

QC20100621Available from: 2010-04-20 Created: 2010-04-16 Last updated: 2010-06-21Bibliographically approved
##### List of papers

This thesis consists of three papers devoted to the study of monotonicity formulas and their applications in elliptic and parabolic free boundary problems. The first paper concerns an inhomogeneous parabolic problem. We obtain global and local almost monotonicity formulas and apply one of them to show a regularity result of a problem that arises in connection with continuation of heat potentials.In the second paper, we consider an elliptic two-phase problem with coefficients bellow the Lipschitz threshold. Optimal $C^{1,1}$ regularity of the solution and a regularity result of the free boundary are established.The third and last paper deals with a parabolic free boundary problem with Hölder continuous coefficients. Optimal $C^{1,1}\cap C^{0,1}$ regularity of the solution is proven.

1. A parabolic almost monotonicity formula$(function(){PrimeFaces.cw("OverlayPanel","overlay325886",{id:"formSmash:j_idt519:0:j_idt523",widgetVar:"overlay325886",target:"formSmash:j_idt519:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. On the two-phase membrane problem with coefficients below the Lipschitz threshold$(function(){PrimeFaces.cw("OverlayPanel","overlay214783",{id:"formSmash:j_idt519:1:j_idt523",widgetVar:"overlay214783",target:"formSmash:j_idt519:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Regularity of a parabolic free boundary problem with Hölder continuous coefficients$(function(){PrimeFaces.cw("OverlayPanel","overlay325918",{id:"formSmash:j_idt519:2:j_idt523",widgetVar:"overlay325918",target:"formSmash:j_idt519:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1256",{id:"formSmash:j_idt1256",widgetVar:"widget_formSmash_j_idt1256",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1309",{id:"formSmash:lower:j_idt1309",widgetVar:"widget_formSmash_lower_j_idt1309",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1310_j_idt1312",{id:"formSmash:lower:j_idt1310:j_idt1312",widgetVar:"widget_formSmash_lower_j_idt1310_j_idt1312",target:"formSmash:lower:j_idt1310:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});