Please use this identifier to cite or link to this item: doi:10.22028/D291-26348
Title: The two-phase membrane problem — regularity of the free boundaries in higher dimensions
Author(s): Shahgholian, Henrik
Uraltseva, Nina
Weiss, Georg S.
Language: English
Year of Publication: 2006
DDC notations: 510 Mathematics
Publikation type: Preprint
Abstract: For the two-phase membrane problem \Delta u=\lambda_{+}\chi_{\{u>0\}}-\lambda_{-}\chi_{\{u<0\}}, where \lambda_{+} and \lambda_{-} are positive Lipschitz functions, 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,\mbox{Dini}}, as shown by a counter-example. As application we obtain a stability result with respect to perturbations of the boundary data.
Link to this record: urn:nbn:de:bsz:291-scidok-46725
hdl:20.500.11880/26404
http://dx.doi.org/10.22028/D291-26348
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 185
Date of registration: 13-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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