Abstract

We show that convex lower semicontinuous functionals defined on functions of bounded variation are characterized by their minima, and we prove a derivation formula which allows an integral representation of such functionals. Applications to relaxation and homogenization are given.

Author information

Contact details are reproduced from the original publication and may be historical.

Andrea Braides

Dipartimento di Elettronica per l’Automazione, Università di Brescia, Via Valotti 9, 25060 Brescia, Italy.

Valeria Chiadò Piat

Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy.

Keywords

  • integral functional
  • lower semicontinuity
  • functions of bounded variation

Suggested citation

A. Braides, V. Chiadò Piat. “A Derivation Formula for Convex Integral Functionals Defined on BV(Ω).” Journal of Convex Analysis 2 (1995), No. 1&2, 69–85. https://doi.org/10.68381/jca02005

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Published by Heldermann Verlag, 1995. Rights now held by Banach Press.