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

Haïm Brezis, Hoai Minh Nguyen

Research output: Contribution to journal › Article

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

Fingerprint

Gamma Convergence
Pointwise Convergence
Nonlinear analysis
Nonlinear Analysis
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.
@article{4963ee3e7d524b9da4b7d089381bf470,
title = "Non-local, non-convex functionals converging to Sobolev norms",
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.",
keywords = "Non-convex, Non-local, Pointwise convergence, Sobolev norms, Γ-convergence",
author = "Ha{\"i}m Brezis and Nguyen, {Hoai Minh}",
year = "2020",
month = "2",
doi = "10.1016/j.na.2019.111626",
language = "English (US)",
volume = "191",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",

}

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

PY - 2020/2

Y1 - 2020/2

N2 - 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.

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.

KW - Non-convex

KW - Non-local

KW - Pointwise convergence

KW - Sobolev norms

KW - Γ-convergence

UR - http://www.scopus.com/inward/record.url?scp=85072543328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072543328&partnerID=8YFLogxK

U2 - 10.1016/j.na.2019.111626

DO - 10.1016/j.na.2019.111626

M3 - Article

AN - SCOPUS:85072543328

VL - 191

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

M1 - 111626

ER -

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

Access to Document