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Advances in Calculus of Variations

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Gradient Young measures, varifolds, and a generalized Willmore functional

Simon Masnou
  • Institut Camille Jordan, Université de Lyon, CNRS UMR 5208, Université Lyon 1, 43 bd du 11 novembre 1918, F-69622 Villeurbanne cedex, France
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/ Giacomo Nardi
Published Online: 2012-11-23 | DOI: https://doi.org/10.1515/acv-2011-0014

Abstract.

Being an open and bounded Lipschitz domain of ℝn, we consider the generalized Willmore functional defined on as

where , , . We propose a new framework that combines varifolds and Young measures to study the relaxation of F in with respect to the strong topology of .

Keywords: Willmore; mean curvature; relaxation; BV; varifolds; Young measures

About the article

Received: 2011-12-11

Revised: 2012-09-06

Accepted: 2012-09-21

Published Online: 2012-11-23

Published in Print: 2013-10-01


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2011-0014.

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Citing Articles

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[1]
Kristian Bredies, Thomas Pock, and Benedikt Wirth
SIAM Journal on Mathematical Analysis, 2015, Volume 47, Number 1, Page 566
[2]
Elie Bretin, Simon Masnou, and Édouard Oudet
Numerische Mathematik, 2015, Volume 131, Number 1, Page 115

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