The quasiconvex hull for the five-gradient problem

Pompe, Waldemar
March 2010
Calculus of Variations & Partial Differential Equations;Mar2010, Vol. 37 Issue 3/4, p461
Academic Journal
In [8 Chapter 4.3] Kirchheim and Preiss gave an example of a set K consisting of five 2 × 2 symmetric matrices without rank-one connections, for which there exists a Lipschitz mapping u satisfying $${Du \in K}$$ . In the present paper we construct the rank-one convex hull of K. As a corollary we obtain that for each $${F \in {\rm int}\,K^{rc}}$$ there exists a Lipschitz mapping u satisfying Moreover, we show that the rank-one convex hull of K and the quasiconvex hull of K are equal.


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