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On the relaxed total variation of singular maps. (English) Zbl 1023.49010
Summary: We consider the total variation functional $TV(u) = \int |\det Du|$ defined on $$W^{1,n} (\Omega,\mathbb{R}^n)$$ for $$\Omega \subset \mathbb{R}^n$$. An extension $$TV^p$$ is defined by relaxation in the weak topology of $$W^{1,p}$$ for $$p<n$$; so the relaxed functional is defined also on maps which may have singularities. In this paper we study the relaxed total variation and compute the functional on 0-homogeneous singular maps.

##### MSC:
 49J45 Methods involving semicontinuity and convergence; relaxation
##### Keywords:
total variation functional; relaxation; singular maps
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