A coarea-type formula for the relaxation of a generalized elastica functional
نویسنده
چکیده
We consider the generalized elastica functional defined on L1(R2) as F(u) = ∫ R2 |∇u|(α +β |div ∇u |∇u| |p)dx, if u ∈ C2(R2), +∞ else, where p > 1, α > 0, β ≥ 0. We study the L1-lower semicontinuous envelope F of F and we prove that, for any u ∈ BV(R2), F(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 {x, u(x)> t}, t ∈ R.
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