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

created by masnou on 20 Dec 2011
modified on 29 Oct 2012

[BibTeX]

Accepted Paper

Inserted: 20 dec 2011
Last Updated: 29 oct 2012

Journal: Journal of Convex Analysis
Year: 2012
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. We prove that its $L^1$-lower semicontinuous envelope at any $u\in BV$ can be represented by a coarea-type formula involving suitable collections of $W^{2,p}$ curves that cover the essential boundaries of the level sets of $u$.