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Journal Articles SIAM Journal on Mathematical Analysis Year : 2008

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.

Dates and versions

hal-00265693 , version 1 (19-03-2008)

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Jean-François Babadjian. Lower semicontinuity of quasiconvex bulk energies in SBV and integral representation in dimension reduction. SIAM Journal on Mathematical Analysis, 2008, 39 (6), pp.1921-1950. ⟨10.1137/060676416⟩. ⟨hal-00265693⟩

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