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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

Luca Mugnai
Max Planck Institute for Mathematics, Inselstr. 22-26, 04103 Leipzig, Germany

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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