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

Haïm Brezis, Hoai Minh Nguyen

Research output: Contribution to journal › Article

1 Citation (Scopus)

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.

Original languageEnglish (US)
Article number111626
JournalNonlinear Analysis, Theory, Methods and Applications
Volume191
DOIs
StatePublished - Feb 2020

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Pointwise Convergence
Continuation
Norm
Family

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Non-convex
  • Non-local
  • Pointwise convergence
  • Sobolev norms
  • Γ-convergence

Cite this

Brezis, Haïm ; Nguyen, Hoai Minh. / Non-local, non-convex functionals converging to Sobolev norms. In: Nonlinear Analysis, Theory, Methods and Applications. 2020 ; Vol. 191.
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Brezis, H & Nguyen, HM 2020, 'Non-local, non-convex functionals converging to Sobolev norms', Nonlinear Analysis, Theory, Methods and Applications, vol. 191, 111626. https://doi.org/10.1016/j.na.2019.111626

Non-local, non-convex functionals converging to Sobolev norms. / Brezis, Haïm; Nguyen, Hoai Minh.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 191, 111626, 02.2020.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Non-local, non-convex functionals converging to Sobolev norms

AU - Brezis, Haïm

AU - Nguyen, Hoai Minh

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AB - 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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KW - Pointwise convergence

KW - Sobolev norms

KW - Γ-convergence

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Brezis H, Nguyen HM. Non-local, non-convex functionals converging to Sobolev norms. Nonlinear Analysis, Theory, Methods and Applications. 2020 Feb;191. 111626. https://doi.org/10.1016/j.na.2019.111626

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