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A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices
Quasiconvexity 2$\times$2 Matrices Rank-one Convexity
2009/1/22
We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence...
Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Uniformly Convex Banach Spaces Norm Total Convexity
2009/1/13
The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for ...