JournalszaaVol. 31, No. 1pp. 75–91

On an Extension of the Space of Bounded Deformations

  • Martin Kružík

    Czech Technical University, Prague, Czech Republic
  • Johannes Zimmer

    University of Bath, United Kingdom
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Abstract

As for functions of bounded variations (BVBV), the space of functions of bounded deformations (BDBD) can be equipped with different topologies. We propose an extension of the traditional space of BDBD 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.

Cite this article

Martin Kružík, Johannes Zimmer, On an Extension of the Space of Bounded Deformations. Z. Anal. Anwend. 31 (2012), no. 1, pp. 75–91

DOI 10.4171/ZAA/1449