A proposal for the modification of the notion of quasiconvexity

Abstract

This note proposes to modify the definition of quasiconvexity of a function f Úìm˜n r Ï ñ Ú ̈ ñ T −ðÙð( on the spaceìm˜n of m ˜ n matrices in such a way that (i) the polyconvexity implies quasiconvexity without any additional measurability or continuity assumption on f and (ii) the pointwise supremum of any family of quasiconvex functions is a quasiconvex… (More)

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