Lower semicontinuity of quasiconvex bulk energies in SBV and integral representation in dimension reduction

Abstract

A result of Larsen concerning the structure of the approximate gradient of certain sequences of functions with Bounded Variation is used to present a short proof of Ambrosio's lower semicontinuity theorem for quasiconvex bulk energies in $SBV$. It enables to generalize to the $SBV$ setting the decomposition lemma for scaled gradients in dimension reduction and also to show that, from the point of view of bulk energies, $SBV$ dimensional reduction problems can be reduced to analogue ones in the Sobolev spaces framework.

arXiv comment25 pages

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