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| HAL: hal-00649363, version 1 |
| arXiv: 1112.2090 |
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| A coarea-type formula for the relaxation of a generalized elastica functional |
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Simon Masnou 1Giacomo Nardi 2 |
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| (2011-12-06) |
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| We consider in R^2 the generalized elastica functional defined, for smooth functions, as the p-elastica energies of the level lines integrated over all levels. Extending the functional to L1, we study its L1-lower semicontinuous envelope and we prove that, for any u in BV, the envelope at u can be represented by a coarea-type formula involving suitable collections of W2,p curves that cover the essential boundaries of the level sets of u. |
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| 1: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie (UPMC) - Paris VI |
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| MMCS |
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| Subject | : | Mathematics/Optimization and Control |
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| elastica – curvature – relaxation – BV |
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| hal-00649363, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00649363 | |
| oai:hal.archives-ouvertes.fr:hal-00649363 | |
| From: Simon Masnou | |
| Submitted on: Thursday, 8 December 2011 23:49:14 | |
| Updated on: Friday, 9 December 2011 14:13:04 | |
