TY  - GEN
T1  - Examples of microstructures related to the theory of martensitic phase transformations
A1  - Fuchs,Martin
A1  - Elfanni,Abdellah
Y1  - 2011/11/22
N2  - We consider the problem
I^{\infty}=\underset{u\in\mathcal{W}}{inf}\underset{\Omega}{\int}\varphi(\nabla u(x,y))dxdy 
in the class \mathcal{W}=\{u\in W^{1,\infty}(\Omega):u/\Gamma_{0}=0,\left|u_{y}\right|=1\, a.e.\}, where \Omega is either the rectangle (0,1)^{2} or the parallelogram \{(x,y)\in\mathbb{R}^{2}:0<y<1,y<x<y+1\} and \Gamma_{0} denotes the boundary part {0}x[0,1] in the first case, for the parallelogram we let \Gamma_{0}=\{(x,x):0\leq x\leq1\}. The function \varphi:\mathbb{R}^{2}\rightarrow[0,\infty) is an elastic potential with wells in (0,\pm1). We prove that I^{\infty}=0  by considering minimizing sequences which differ substantially for both cases.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2011/4354
ER  -