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Rank-one-convex and Quasiconvex Envelopes for Functions Depending on Quadratic Forms
rank-one-convex quasiconvex envelope quadratic form James-Ericksen function Pipkin's formula
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2009/2/5
In this paper we are interested in functions defined, on a set of matrices, by the mean of quadratic forms and we compute the rank-one-convex, quasiconvex, polyconvex and convex envelopes of these fun...
A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices
Quasiconvexity 2$\times$2 Matrices Rank-one Convexity
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2009/1/22
We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence...
Rank-One Connections at Infinity and Quasiconvex Hulls
Rank-One Infinity Quasiconvex Hulls
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2009/1/13
We define $p$-rank-one connections at infinity for an unbounded set $K$ in $M^{N\times n}$ and show that the quasiconvex hull $Q_p(K)$ may be bigger than $K$ if $K$ has a $p$-rank-one connection, wher...