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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
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