Integral representation and relaxation for functionals defined on measures

Ennio De Giorgi; Luigi Ambrosio; Giuseppe Buttazzo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1987)

  • Volume: 81, Issue: 1, page 7-13
  • ISSN: 0392-7881

Abstract

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Given a separable metric locally compact space Ω , and a positive finite non-atomic measure λ on Ω , we study the integral representation on the space of measures with bounded variation Ω of the lower semicontinuous envelope of the functional F ⁢ ( u ) = ∫ Ω f ⁢ ( x , u ) ⁢ 𝑑 λ    u ∈ L 1 ⁢ ( Ω , λ , ℝ n ) with respect to the weak convergence of measures.

How to cite

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De Giorgi, Ennio, Ambrosio, Luigi, and Buttazzo, Giuseppe. "Integral representation and relaxation for functionals defined on measures." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 81.1 (1987): 7-13. <http://eudml.org/doc/289114>.

@article{DeGiorgi1987,
abstract = {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.},
author = {De Giorgi, Ennio, Ambrosio, Luigi, Buttazzo, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Relaxation; Integral representation; Measures},
language = {eng},
month = {3},
number = {1},
pages = {7-13},
publisher = {Accademia Nazionale dei Lincei},
title = {Integral representation and relaxation for functionals defined on measures},
url = {http://eudml.org/doc/289114},
volume = {81},
year = {1987},
}

TY - JOUR
AU - De Giorgi, Ennio
AU - Ambrosio, Luigi
AU - Buttazzo, Giuseppe
TI - Integral representation and relaxation for functionals defined on measures
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1987/3//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 1
SP - 7
EP - 13
AB - 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.
LA - eng
KW - Relaxation; Integral representation; Measures
UR - http://eudml.org/doc/289114
ER -

References

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