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Journal of Convex Analysis 06 (1999), No. 1, 141--162
Copyright Heldermann Verlag 1999



On a Non-Standard Convex Regularization and the Relaxation of Unbounded Integral Functionals of the Calculus of Variations

Luciano Carbone
Dip. di Matematica e Applicazioni, UniversitÓ di Napoli, Via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy

Riccardo De Arcangelis
Dip. di Matematica e Applicazioni, UniversitÓ di Napoli, Via Cintia, Complesso Monte S. Angelo, 80126 Napoli, Italy



A new convex regularization procedure for a function, appearing in the study of some sequential relaxation processes for integral functionals of the Calculus of Variations, is introduced and studied. The connections with the usual convex, lower semicontinuous enveloping are investigated, together with examples showing that they are different. Applications to integral representation problems, and to sequential relaxation processes are also given.

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