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The quasiconvex hull for the five-gradient problem.
- Source :
-
Calculus of Variations & Partial Differential Equations . Mar2010, Vol. 37 Issue 3/4, p461-473. 13p. 7 Diagrams. - Publication Year :
- 2010
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09442669
- Volume :
- 37
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Calculus of Variations & Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 47955917
- Full Text :
- https://doi.org/10.1007/s00526-009-0272-z