TY  - GEN
T1  - The two-phase membrane problem — regularity of the free boundaries in higher dimensions
A1  - Shahgholian,Henrik
A1  - Uraltseva,Nina
A1  - Weiss,Georg S.
Y1  - 2012/03/13
N2  - 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.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4672
ER  -