Geodesic
A New $L^1$-Lower Semicontinuity Result
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 797-818 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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The aim of this work is to prove a chain rule and an $L^1$-lower semicontinuity theorems for integral functional defined on $BV(\Omega)$. Moreover we apply this result in order to obtain new relaxation and $\Gamma$-convergence result without any coerciveness and any continuity assumption of the integrand $f(x, s, p)$ with respect to the variable $s$. 
@article{BUMI_2007_8_10B_3_a23,
     author = {Graziani, Daniele},
     title = {A {New} $L^1${-Lower} {Semicontinuity} {Result}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {797--818},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {3},
     zbl = {1181.49012},
     mrnumber = {2507897},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a23/}
}
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Graziani, Daniele. A New $L^1$-Lower Semicontinuity Result. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 797-818. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a23/