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Wavelet analogue of the Ginzburg–Landau energy and its Γ-convergence

2010
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Interfaces and free boundaries (Print)
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This paper considers a wavelet analogue of the classical Ginzburg-Landau energy, where the H 1 seminorm is replaced by the Besov seminorm defined via an arbitrary regular wavelet. We prove that functionals of this type Γ -converge to a weighted analogue of the TV functional on characteristic functions of finite-perimeter sets. The Γ -limiting functional is defined explicitly, in terms of the wavelet that is used to define the energy. We show that the limiting energy is none other than the

doi:10.4171/ifb/243
fatcat:qqiuc5pvyrbanjg6ojq46k7jzu