15 April 2011 Γ-convergence, Sobolev norms, and BV functions
Hoai-Minh Nguyen
Author Affiliations +
Duke Math. J. 157(3): 495-533 (15 April 2011). DOI: 10.1215/00127094-1272921

Abstract

We prove that the family of functionals (Iδ) defined by Iδ(g)=RN×RN|g(x)-g(y)|>δδp|x-y|N+pdxdy,gLp(RN), for p1 and δ>0, Γ-converges in Lp(RN), as δ goes to zero, when p1. Hereafter | | denotes the Euclidean norm of RN. We also introduce a characterization for bounded variation (BV) functions which has some advantages in comparison with the classic one based on the notion of essential variation on almost every line.

Citation

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Hoai-Minh Nguyen. "Γ-convergence, Sobolev norms, and BV functions." Duke Math. J. 157 (3) 495 - 533, 15 April 2011. https://doi.org/10.1215/00127094-1272921

Information

Published: 15 April 2011
First available in Project Euclid: 1 April 2011

zbMATH: 1221.28011
MathSciNet: MR2785828
Digital Object Identifier: 10.1215/00127094-1272921

Subjects:
Primary: 28A20
Secondary: 26A24 , 26A84

Rights: Copyright © 2011 Duke University Press

Vol.157 • No. 3 • 15 April 2011
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