CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt149",{id:"formSmash:upper:j_idt149",widgetVar:"widget_formSmash_upper_j_idt149",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt150_j_idt152",{id:"formSmash:upper:j_idt150:j_idt152",widgetVar:"widget_formSmash_upper_j_idt150_j_idt152",target:"formSmash:upper:j_idt150:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Regularity and boundary behavior of solutions to complex Monge–Ampère equationsPrimeFaces.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();
}
}
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Uppsala: Matematiska institutionen , 2002. , p. 95
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 21
##### Keywords [en]

Mathematics, Complex Monge--Ampère operator, interior regularity, plurisubharmonic function, blow-up rate of solutions, bounded plurisubharmonic exhaustion function, globally Lipschitz, strongly pseudoconvex domain, hyperconvex domain, Bergman kernel
##### Keywords [sv]

MATEMATIK
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-1603ISBN: 91-506-1533-5 (print)OAI: oai:DiVA.org:uu-1603DiVA, id: diva2:161194
##### Public defence

2002-02-08, Rum 247, Hus 2, Polacksbacken, Uppsala, 13:15
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt459",{id:"formSmash:j_idt459",widgetVar:"widget_formSmash_j_idt459",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt470",{id:"formSmash:j_idt470",widgetVar:"widget_formSmash_j_idt470",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true}); Available from: 2002-01-18 Created: 2002-01-18Bibliographically approved

In the theory of holomorphic functions of one complex variable it is often useful to study subharmonic functions. The subharmonic can be described using the Laplace operator. When one studies holomorphic functions of several complex variables one should study the plurisubharmonic functions instead. Here the complex Monge--Ampère operator has a role similar to that of the Laplace operator in the theory of subharmonic functions. The complex Monge--Ampère operator is nonlinear and therefore it is not as well understood as the Laplace operator. We consider two types of boundary value problems for the complex Monge--Ampere equation in certain pseudoconvex domains. In this thesis the right-hand side in the Monge--Ampère equation will always be smooth, strictly positive and meet a monotonicity condition. The first type of boundary value problem we consider is a Dirichlet problem where we look for plurisubharmonic solutions which are zero on the boundary of the domain. We show that this problem has a unique smooth solution if the domain has a smooth bounded plurisubharmonic exhaustion function which is globally Lipschitz and has Monge--Ampère mass larger than one everywhere. We obtain some results on which domains have such a bounded exhaustion function. The second type of boundary value problem we consider is a boundary blow-up problem where we look for plurisubharmonic solutions which tend to infinity at the boundary of the domain. Here we also assume that the right-hand side in the Monge--Ampère equation satisfies a growth condition. We study this problem in strongly pseudoconvex domains with smooth boundary and show that it has solutions which are Hölder continuous with arbitrary Hölder exponent α, 0 ≤ α < 1. We also show a uniqueness result. A result on the growth of the solutions is also proved. This result is used to describe the boundary behavior of the Bergman kernel.

isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1295",{id:"formSmash:j_idt1295",widgetVar:"widget_formSmash_j_idt1295",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1348",{id:"formSmash:lower:j_idt1348",widgetVar:"widget_formSmash_lower_j_idt1348",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1349_j_idt1351",{id:"formSmash:lower:j_idt1349:j_idt1351",widgetVar:"widget_formSmash_lower_j_idt1349_j_idt1351",target:"formSmash:lower:j_idt1349:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});