Characterization of gradient young measures generated by homeomorphisms in the plane

Benešová, Barbora; Kružík, Martin

doi:10.1051/cocv/2015003

Benešová, Barbora ^1,² ; Kružík, Martin ^1,^2,³

¹ Department of Mathematics I, RWTH Aachen University, 52056 Aachen, Germany
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

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 267-288.

Résumé

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.

Reçu le : 2014-05-13

MR Zbl

DOI : 10.1051/cocv/2015003

Classification : 49J45, 35B05
Mots clés : Orientation-preserving mappings, Young measures

Affiliations des auteurs :

Benešová, Barbora ^{1, 2} ; Kružík, Martin ^{1, 2, 3}

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     title = {Characterization of gradient young measures generated by homeomorphisms in the plane},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {267--288},
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     url = {http://archive.numdam.org/articles/10.1051/cocv/2015003/}
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Benešová, Barbora; Kružík, Martin. Characterization of gradient young measures generated by homeomorphisms in the plane. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 267-288. doi : 10.1051/cocv/2015003. http://archive.numdam.org/articles/10.1051/cocv/2015003/

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