Abstract

We prove a new representation result for the L1L^1-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.

Author information

Contact details are reproduced from the original publication and may be historical.

Giovanni Bellettini

Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

belletti@mat.uniroma2.it

Luca Mugnai

Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, 04103 Leipzig, Germany

mugnai@mis.mpg.de

Keywords

  • Varifolds
  • representation result
  • L-1-lower semicontinuous envelope
  • elastica functional
  • minimum problem
  • Sobolev-type submanifolds

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Suggested citation

G. Bellettini, L. Mugnai. “A Varifolds Representation of the Relaxed Elastica Functional.” Journal of Convex Analysis 14 (2007), No. 3, 543–564. https://doi.org/10.68381/jca14033

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press.