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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with ≥ . The most important novelty is that the energy features a singular set
of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()
−convergence, in the same spirit of the work by Ambrosio and Tortorelli [L. Ambrosio and...
Given an open set Ω ⊂ Rm and n > 1, we introduce the new spaces GBnV(Ω) of Generalized functions of bounded higher variation and GSBnV(Ω) of Generalized special functions of bounded higher variation that generalize, respectively, the space BnV introduced by Jerrard and Soner in [43] and the corresponding SBnV space studied by De Lellis in [24]. In this class of spaces, which allow as in [43] the description of singularities of codimension n, the distributional jacobian Ju need not have finite...
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