Characterization of Gradient Young Measures (Caracterisation des measures deYoung associees a un gradient)

摘要

Oscillatory properties of a weak convergent sequence of functions may besummarized by the parametrized measure of Young measure it generates. When such a measure is generated by a sequence of gradients, for example, when it arises from a minimizing sequence in a problem in the calculus of variations, it must have special properties. Such a measure is called a gradient parametrized measure or gradient Young measure. The purpose of this Note is to establish that a measure with compact support is a gradient parametrized measure if and only if it obeys Jensen's inequality for all quasiconvex functions.