A coarea-type formula for the relaxation of a generalized elastica functional

Details A coarea-type formula for the relaxation of a generalized elastica functional A coarea-type formula for the relaxation of a generalized elastica functional

2011-12-09

arxiv.org/abs/1112.2090v1

Mathematics

Optimization and Control

34 pages

Scientific paper

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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