Please use this identifier to cite or link to this item: doi:10.22028/D291-26192
Title: Examples of microstructures related to the theory of martensitic phase transformations
Author(s): Fuchs, Martin
Elfanni, Abdellah
Language: English
Year of Publication: 2001
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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.
Link to this record: urn:nbn:de:bsz:291-scidok-43546
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 35
Date of registration: 22-Nov-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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