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August 17, 201916 citationsOpen Access

Non-local, non-convex functionals related to Sobolev norms

HBHaı̈m BrezisHNHoài-Minh Nguyên

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Abstract

We study the pointwise convergence and the Γ-convergence of a family of non-local, non-convex functionals Λδ in Lp(Ω) for p>1. We show that the limits are multiples of ∫Ω|∇u|p. This is a continuation of our previous work where the case p=1 was considered.

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Cite This Study

Brezis et al. (2019) studied this question.

synapsesocial.com/papers/6a1029f8d8c5cf602efdc81bhttps://doi.org/10.1016/j.na.2019.111626
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