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: | Other |
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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File | Description | Size | Format | |
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preprint_185_06.pdf | 236,49 kB | Adobe PDF | View/Open |
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