Please use this identifier to cite or link to this item:
doi:10.22028/D291-26210
Title: | Microstructures corresponding to curved austenite-martensite interfaces |
Author(s): | Elfanni, Abdellah Fuchs, Martin |
Language: | English |
Year of Publication: | 2002 |
Free key words: | elastic energy minimizing sequences Young measures |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
Abstract: | 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}. |
Link to this record: | urn:nbn:de:bsz:291-scidok-43857 hdl:20.500.11880/26266 http://dx.doi.org/10.22028/D291-26210 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 60 |
Date of registration: | 2-Dec-2011 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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