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The two-phase membrane problem - An intersection-comparison approach to the regularity at branch points
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2006 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 205, no 2, 487-503 p.Article in journal (Refereed) Published
Abstract [en]

For the two-phase membrane problem Delta u = (lambda)+/2 chi{u>0} - (lambda)-/2 chi{u<0}, where lambda(+) > 0 and lambda(-) > 0, we prove in two dimensions that the free boundary is in a neighborhood of each branch point the union of two C-1-graphs. We also obtain a stability result with respect to perturbations of the boundary data. Our analysis uses an intersection-comparison approach based on the Aleksandrov reflection.

Place, publisher, year, edition, pages
2006. Vol. 205, no 2, 487-503 p.
Keyword [en]
free boundary, singular point, branch point, membrane, obstacle problem, regularity, global solution, blow-up, monotonicity formula, Aleksandrov reflection, aleksandrov reflection, obstacle-problem, free-boundary, 2 phases, equation, singularities, evolution
URN: urn:nbn:se:kth:diva-16008DOI: 10.1016/j.aim.2005.07.015ISI: 000240852300005ScopusID: 2-s2.0-33747200807OAI: diva2:334050
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Shahgholian, Henrik
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