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Journal of Convex Analysis 14 (2007), No. 3, 543--564
Copyright Heldermann Verlag 2007



A Varifolds Representation of the Relaxed Elastica Functional

Giovanni Bellettini
Dipartimento di Matematica, UniversitÓ di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy
belletti@mat.uniroma2.it

Luca Mugnai
Max Planck Institute for Mathematics, Inselstr. 22-26, 04103 Leipzig, Germany
mugnai@mis.mpg.de



We prove a new representation result for the L1-lower semicontinuous envelope of the elastica functional in terms of a minimum problem over a suitable class of varifolds. We also show a representation result in a suitable class of Sobolev-type submanifolds.

Keywords: Varifolds, representation result, L-1-lower semicontinuous envelope, elastica functional, minimum problem, Sobolev-type submanifolds.

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