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

Haïm Brezis; Hoai Minh Nguyen

doi:10.1016/j.na.2019.111626

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

Haïm Brezis, Hoai Minh Nguyen

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article

2 Scopus citations

Abstract

We study the pointwise convergence and the Γ-convergence of a family of non-local, non-convex functionals Λ_δ in L^p(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 language	English (US)
Article number	111626
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	191
DOIs	https://doi.org/10.1016/j.na.2019.111626
State	Published - Feb 2020

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All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

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

Cite this

Brezis, H., & Nguyen, H. M. (2020). Non-local, non-convex functionals converging to Sobolev norms. Nonlinear Analysis, Theory, Methods and Applications, 191, [111626]. https://doi.org/10.1016/j.na.2019.111626

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10.1016/j.na.2019.111626