TY  - GEN
T1  - Microstructures corresponding to curved austenite-martensite interfaces
A1  - Elfanni,Abdellah
A1  - Fuchs,Martin
Y1  - 2011/12/02
N2  - Let \Omega\subset\mathbb{R}^{2} denote a bounded Lipschitz domain and consider some portion \Gamma_{0} of  \partial\Omega representing the austenite-twinned martensite interface which is not assumed to be a straight segment. We prove \underset{u\in\mathcal{W}(\Omega)}{inf}\int_{\Omega}\varphi(\nabla u(x,y))dxdy=0 for an elastic energy density \varphi:\mathbb{R}^{2}\rightarrow[0,\infty) such that \varphi(0,\pm1)=0. Here \mathcal{W}(\Omega) consist of all functions u from the Sobolev class W^{1,\infty}(\Omega) such that \left|u_{y}\right|=1 a.e. on \Omega together with u=0 on \Gamma_{0}. Moreover some minimizing sequences vanishing on the whole boundary \partial\Omega are constructed, that is, one can even take \Gamma_{0}=\partial\Omega. We also show that the existence or nonexistence of minimizers depends on the shape of the austenite-twinned martensite interface \Gamma_{0}.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2011/4385
ER  -