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arXiv · 1308.3377

Characterization of gradient Young measures generated by homeomorphisms in the plane

Barbora Benešová·Martin Kružík
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Abstract

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.

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Barbora Benešová, Martin Kružík. 2015-01-26. Characterization of gradient Young measures generated by homeomorphisms in the plane. https://doi.org/10.1051/cocv%2F2015003

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