Γ-convergence of non-local, non-convex functionals in one dimension.

We study the Γ -convergence of a family of non-local, non-convex functionals in L p (I) for p ≥ 1 , where I is an open interval. We show that the limit is a multiple of the W 1 , p (I) semi-norm to the power p when p > 1 (respectively, the B V (I) semi-norm when p = 1). In dimension one, this extends earlier results which required a monotonicity condition. [ABSTRACT FROM AUTHOR]