Abstract
We study the [Formula: see text]-convergence of a family of non-local, non-convex functionals in [Formula: see text] for [Formula: see text], where [Formula: see text] is an open interval. We show that the limit is a multiple of the [Formula: see text] semi-norm to the power [Formula: see text] when [Formula: see text] (respectively, the [Formula: see text] semi-norm when [Formula: see text]). In dimension one, this extends earlier results which required a monotonicity condition.