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arXiv · 1909.02162

$\Gamma$-convergence of non-local, non-convex functionals in one dimension

Haim Brezis·Hoai-Minh Nguyen
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Abstract

We study the $\Gamma$-convergence of a family of non-local, non-convex functionals in $L^p(I)$ for $p \ge 1$, 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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Haim Brezis, Hoai-Minh Nguyen. 2019-09-05. $\Gamma$-convergence of non-local, non-convex functionals in one dimension. https://arxiv.org/abs/1909.02162

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