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

By Simon Masnou and Giacomo Nardi


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.Comment: 34 page

Topics: Mathematics - Optimization and Control
Year: 2011
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