CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt184",{id:"formSmash:upper:j_idt184",widgetVar:"widget_formSmash_upper_j_idt184",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt192_j_idt200",{id:"formSmash:upper:j_idt192:j_idt200",widgetVar:"widget_formSmash_upper_j_idt192_j_idt200",target:"formSmash:upper:j_idt192:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficientsPrimeFaces.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}); PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt367",{id:"formSmash:j_idt367",widgetVar:"widget_formSmash_j_idt367",onLabel:"Hide others and affiliations",offLabel:"Show others and affiliations"});
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}); 2007 (English)Other (Other academic)
##### Abstract [en]

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

2007. , p. 60
##### National Category

Mathematical Analysis
##### Identifiers

URN: urn:nbn:se:su:diva-20728OAI: oai:DiVA.org:su-20728DiVA, id: diva2:187254
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt987",{id:"formSmash:j_idt987",widgetVar:"widget_formSmash_j_idt987",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1004",{id:"formSmash:j_idt1004",widgetVar:"widget_formSmash_j_idt1004",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1012",{id:"formSmash:j_idt1012",widgetVar:"widget_formSmash_j_idt1012",multiple:true});
Available from: 2007-11-29 Created: 2007-11-29Bibliographically approved

We consider divergence form elliptic operators of the form $L=-\dv A(x)\nabla$, defined in $R^{n+1} = \{(x,t)\in R^n \times R \}$, $n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic, complex and $t$-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on $L^2(\mathbb{R}^{n})=L^2(\partial\mathbb{R}_{+}^{n+1})$, is stable under complex, $L^{\infty}$ perturbations of the coefficient matrix. Using a variant of the $Tb$ Theorem, we also prove that the layer potentials are bounded and invertible on $L^2(\mathbb{R}^n)$ whenever $A(x)$ is real and symmetric (and thus, by our stability result, also when $A$ is complex, $\Vert A-A^0\Vert_{\infty}$ is small enough and $A^0$ is real, symmetric, $L^{\infty}$ and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with $L^2$ (resp. $\dot{L}^2_1)$ data, for small complex perturbations of a real symmetric matrix. Previously, $L^2$ solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients $A_{j,n+1}=0=A_{n+1,j}$, $1\leq j\leq n$, which corresponds to the Kato square root problem.

urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt2096",{id:"formSmash:j_idt2096",widgetVar:"widget_formSmash_j_idt2096",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt2149",{id:"formSmash:lower:j_idt2149",widgetVar:"widget_formSmash_lower_j_idt2149",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt2150_j_idt2152",{id:"formSmash:lower:j_idt2150:j_idt2152",widgetVar:"widget_formSmash_lower_j_idt2150_j_idt2152",target:"formSmash:lower:j_idt2150:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});