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The Two-Phase Membrane Problem-Regularity of the Free Boundaries in Higher Dimensions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2007 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Article in journal (Refereed) Published
Abstract [en]

For the two-phase membrane problem Delta u = lambda(+chi{u > 0}) -lambda(-chi{u < 0}), where lambda(+) and lambda(-) are positive Lipschitz functions, and we prove in higher dimensions that the free boundary is in a neighborhood of each "branch point" the union of two C-1-graphs. The result is optimal in the sense that these graphs are in general not of class C-1,C-Dini, as shown by a counter-example. As an application we obtain a stability result with respect to perturbations of the boundary data.

Place, publisher, year, edition, pages
URN: urn:nbn:se:kth:diva-16286DOI: 10.1093/imrn/rnm026ISI: 000206288300026ScopusID: 2-s2.0-77949653659OAI: diva2:334328
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Shahgholian, Henrik
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