Journal of Convex Analysis 12 (2005), No. 1, 173--185
Copyright Heldermann Verlag 2005
On L1-Lower Semicontinuity in BV
Virginia De Cicco
Universita di Roma, Dip. di Metodi e Modelli Matematici per le Scienze Applicate, Via Scarpa 16, 00161 Roma, Italy
decicco@dmmm.unirom1.it
Nicola Fusco
Universita di Napoli, Dipartimento di Matematica e Applicazioni, Via Cinzia, 80126 Napoli, Italy
n.fusco@unina.it
Anna Verde
Universita di Napoli, Dipartimento di Matematica e Applicazioni, Via Cinzia, 80126 Napoli, Italy
anverde@unina.it
A new lower semicontinuity theorem for integral functionals defined on the space BV of functions of bounded variation is proved. This result is obtained by replacing the continuity of the energy density f with respect to the space variable x with a weak differentiability assumption. The proof is based on a new integration by parts formula in the space BV which does not seem to be contained in any of the similar results known in the literature and which could be of independent interest.
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