Abstract
Following a notation introduced by De Giorgi, we denote by “free discontinuity problems” all the problems in the calculus of variations where the unknown is a pair (uK)withKvarying in a class of closed subsets of a fixed open set Ω ⊂ Rnand u: Ω\K→Rm is a function in some function space (e.g., u ∈ C1,p (Ω\K))or u ∈W 1,p n(Ω\K)).
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