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Article Dans Une Revue Bollettino dell'Unione Matematica Italiana Année : 2014

Radial representation of lower semicontinuous envelope

Résumé

We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper semicontinuity which plays the role of convexity, and allows to prove a radial representation result for nonconvex functions. An application to the relaxation of multiple integrals with constraints on the gradient is given.
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Dates et versions

hal-00958312 , version 1 (05-04-2016)

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Omar Anza Hafsa, Jean-Philippe Mandallena. Radial representation of lower semicontinuous envelope. Bollettino dell'Unione Matematica Italiana, 2014, 7 (1), pp.1-18. ⟨10.1007/s40574-014-0001-1⟩. ⟨hal-00958312⟩
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