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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 10, Issue 2

# Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation

Gianni Dal Maso
/ Gianluca Orlando
Published Online: 2016-04-07 | DOI: https://doi.org/10.1515/acv-2015-0036

## Abstract

We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to ${L}^{1}$ convergence.

MSC 2010: 49J45; 26B30

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Revised: 2016-02-06

Accepted: 2016-03-05

Published Online: 2016-04-07

Published in Print: 2017-04-01

This material is based on work supported by the Italian Ministry of Education, University, and Research under the project “Calculus of Variations” (PRIN 2010-11) and by the European Research Council under Grant No. 290888 “Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture”. The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Citation Information: Advances in Calculus of Variations, Volume 10, Issue 2, Pages 183–207, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258,

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