Mathematical Institute, Acad. Sci.of the
Czech Republic, 115 67 PRAHA 1, Zitna 25, Czech Republic, e-mail: silhavy@math.cas.cz
Summary:
It is noted that the quasiconvex hull of the euclidean distance from a compact nonconvex quasiconvex $O(n)$ invariant subset of the space $M^{n\times n}$ of $n\times n$ real matrices is not polyconvex. This provides an example of an $O(n)$ invariant quasiconvex (and hence rank 1 convex) function that is not polyconvex and answers a recent question by Dacorogna & Marcellini and Cardaliaguet & Tahraoui.
Keywords: quasiconvexity, polyconvexity, rank 1 convexity
Mathematics Subject Classification
2000: 49J45
[Mathematical Institute AS CR] [Publications of the Institute] [Preprint series]
