Abstract

We study the Γ-convergence of a family of non-local, non-convex functionals in Lp(I) for p≥1, where I is an open interval. We show that the limit is a multiple of the W1,p(I) semi-norm to the power p when p>1 (respectively, the BV(I) semi-norm when p=1). In dimension one, this extends earlier results which required a monotonicity condition.