Published Paper
Inserted: 12 nov 2002
Last Updated: 30 nov 2016
Journal: manuscripta mathematica
Volume: 111
Pages: 499-512
Year: 2003
Doi: 10.1007/s00229-003-0381-5
Abstract:
We consider the Total Variation functional $TV(u) = \int \vert \det Du\vert$ which is defined on $W^{1,n}(\Omega,{\mathbf R}^n)$ for $\Omega\subset {\mathbf R}^n$. 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 find many useful tools to compute the functional on maps which have a singularity in one point.
Keywords: relaxation, Jacobian, Total variation
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