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Zeitschrift für Analysis und ihre Anwendungen

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Volume 31, Issue 1, 2012, pp. 75–91
DOI: 10.4171/ZAA/1449

Published online: 2011-12-27

On an Extension of the Space of Bounded Deformations

Martin Kružík[1] and Johannes Zimmer[2]

(1) Czech Technical University, Prague, Czech Republic
(2) University of Bath, United Kingdom

As for functions of bounded variations ($BV$), the space of functions of bounded deformations ($BD$) can be equipped with different topologies. We propose an extension of the traditional space of $BD$ functions equipped with the weak-$\star$ topology. It is shown that in this fine extension, both compactness and weak-$\star$ continuity of the trace hold under weak assumptions. This is relevant for applications, where the specimen is typically exposed to forces on the boundary. We give an application to a functional with a linearly growing energy density.

Keywords: Bounded sequences of symmetrised gradients, bounded deformation, concentrations and oscillations, quasiconvexity

Kružík Martin, Zimmer Johannes: On an Extension of the Space of Bounded Deformations. Z. Anal. Anwend. 31 (2012), 75-91. doi: 10.4171/ZAA/1449