Γ-convergence, Sobolev norms, and BV functions
نویسنده
چکیده
We prove that the family of functionals (Iδ) defined by Iδ(g) = ∫∫ RN×RN |g(x)−g(y)|>δ δ |x− y|N+p dx dy, ∀ g ∈ L(R ), for p ≥ 1 and δ > 0, Γ-converges in L(R ), as δ goes to 0, when p ≥ 1. Hereafter | | denotes the Euclidean norm of R . We also introduce a characterization for BV functions which has some advantages in comparison with the classic one based on the notion of essential variation on a.e. line.
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