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

2019/09/05 by Haïm Brézis, Brezis, Haim, Hoài-Minh Nguyên +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1909.02162

openalex publication_date 2019/09/05 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

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 (resp. the BV(I) semi-norm when p=1). In dimension one, this extends earlier results which required a monotonicity condition.

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