On the Stability of Quasiconvex Hulls 1998
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(0) (0 Votes)Views: (1011) Date: (13-05-09) Pages: () -
Author: by Kewei Zhang Kewei Zhang
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Abstract: . We study the stability problem of the quasiconvex hull Q(K) for a compact set K ae M N \Thetan with respect to K by using Hausdorff metric over compact sets. We introduce various stability criteria and examine some examples including the quasiconvex hull for the two-well problem in modelling martensitic phase transformations. x1. Introduction. In this paper we use the Hausdorff metric on space of compact subsets in M N \Thetan (the space of N \Theta n real matrices) to study the stability of quasiconvex hulls. We introduce various stability criteria and establish some stability results for quasiconvex hulls studied in martensitic phase transformations. For a compact subset K ae M N \Thetan , we may define its quasiconvex hull Q(K) by cosets of quasiconvex functions [Sv2], or alternatively, by direct quasiconvex relaxations of the distance functions to the set [Z3]. In fact, the study of quasiconvex hulls in M N \Thetan goes back to L. Tartar [T1] and J. M. Ball [Bl2]. A comp...
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