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       font style='font-size:12px;'> 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...

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A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices     Quasiconvexity  2$\times$2 Matrices  Rank-one Convexity       font style='font-size:12px;'> 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...

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Rank-One Connections at Infinity and Quasiconvex Hulls     Rank-One  Infinity  Quasiconvex Hulls       font style='font-size:12px;'> 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...

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