Geodesic
Integral representation and relaxation for functionals defined on measures
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 81 (1987) no. 1, pp. 7-13 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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Given a separable metric locally compact space $\Omega$, and a positive finite non-atomic measure $\lambda$ on $\Omega$, we study the integral representation on the space of measures with bounded variation $\Omega$ of the lower semicontinuous envelope of the functional $$F(u) = \int_{\Omega} f(x,u) d\lambda \qquad u \in L^{1}(\Omega,\lambda,\mathbb{R}^{n})$$ with respect to the weak convergence of measures. 
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     title = {Integral representation and relaxation for functionals defined on measures},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
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De Giorgi, Ennio; Ambrosio, Luigi; Buttazzo, Giuseppe. Integral representation and relaxation for functionals defined on measures. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 81 (1987) no. 1, pp. 7-13. http://geodesic.mathdoc.fr/item/RLINA_1987_8_81_1_a1/

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