Volume 22, Number 1, January-March 2016
|Page(s)||267 - 288|
|Published online||28 January 2016|
Characterization of gradient young measures generated by homeomorphisms in the plane∗
Department of Mathematics I, RWTH Aachen University,
2 Institute for Mathematics, University of Würzburg, Emil-Fischer-Straße 40, 97074 Würzburg, Germany
3 Institute of Information Theory and Automation, Czech Academy of Sciences, Pod vodárenskou věží 4, CZ-182 08 Praha 8 Czech Republic & Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29 Praha 6, Czech Republic
Revised: 14 November 2014
We characterize Young measures generated by gradients of bi-Lipschitz orientation-preserving maps in the plane. This question is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of the admissible deformations are key requirements. These results enable us to derive new weak∗ lower semicontinuity results for integral functionals depending on gradients. As an application, we show the existence of a minimizer for an integral functional with nonpolyconvex energy density among bi-Lipschitz homeomorphisms.
Mathematics Subject Classification: 49J45 / 35B05
Key words: Orientation-preserving mappings / Young measures
© EDP Sciences, SMAI 2016
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