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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 1
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Articles

Young measures supported on invertible matrices

Barbora BenešováDepartment of Ultrasound Methods, Institute of Thermomechanics of the ASCR, Dolejškova 5 CZ-182 08, Praha 8, Czech Republic;.;Faculty of Mathematics and Physics, Charles University, Sokolovská 83 CZ-186 75, Praha 8, Czech Republic;.;Department of Mathematics I, D-52056 RWTH Aachen, Aachen, Germany.
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Martin KružíkDepartment of Decision Making, Institute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, CZ-182 08 Praha 8, Czech Republic;.;Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 Praha 6, Czech Republic.Correspondence[email protected]
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Gabriel PathóFaculty of Mathematics and Physics, Charles University, Sokolovská 83 CZ-186 75, Praha 8, Czech Republic;.;Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 Praha 6, Czech Republic.
Pages 105-123 | Received 13 Dec 2012, Accepted 13 Dec 2012, Published online: 04 Mar 2013
 
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Abstract

Motivated by variational problems in non-linear elasticity, we explicitly characterize the set of Young measures generated by gradients of a uniformly bounded sequence in where the inverted gradients are also bounded in . This extends the original results due to the studies Kinderlehrer and Pedregal. Besides, we completely describe Young measures generated by a sequence of matrix-valued mappings , such that is bounded, too, and the generating sequence satisfies the constraint .

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Acknowledgments

BB was supported by the grants P201/10/0357 (GA ČR), 41110 (GAUK ČR) and the plan AV0Z20760514 (ČR). MK also thanks for support through the grant P201/12/0671 (GA ČR). GP wishes to thank GA ČR for the support through the project P105/11/0411 and to GAUK for the support through SVV-2012-265310.

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