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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang


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1864-8266
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Volume 6, Issue 1

Issues

On the non-occurrence of the Lavrentiev phenomenon

Giovanni Bonfanti
  • Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy
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/ Arrigo Cellina
  • Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy
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Published Online: 2013-01-03 | DOI: https://doi.org/10.1515/acv-2011-0002

Abstract.

We show that the Lavrentiev phenomenon does not occur for functionals of the form

where L is an arbitrary convex function, provided that both and u0 are of class C2.

Keywords: Calculus of variations; Lavrentiev phenomenon; regularity

About the article

Received: 2011-06-23

Revised: 2012-03-14

Accepted: 2012-04-03

Published Online: 2013-01-03

Published in Print: 2013-01-01


Citation Information: , Volume 6, Issue 1, Pages 93–121, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2011-0002.

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Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Pierre Bousquet, Carlo Mariconda, and Giulia Treu
Set-Valued and Variational Analysis, 2015, Volume 23, Number 1, Page 55
[2]
Pierre Bousquet, Carlo Mariconda, and Giulia Treu
Journal of Functional Analysis, 2014, Volume 266, Number 9, Page 5921
[3]
Giovanni Bonfanti and Arrigo Cellina
SIAM Journal on Control and Optimization, 2013, Volume 51, Number 2, Page 1639

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