As for functions of bounded variations (), the space of functions of bounded deformations () can be equipped with different topologies. We propose an extension of the traditional space of functions equipped with the weak- topology. It is shown that in this fine extension, both compactness and weak- 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. 75–91DOI 10.4171/ZAA/1449