Calculus of Variations and Geometric Measure Theory

G. Dal Maso - G. Orlando - R. Toader

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

created by orlando on 24 Sep 2015
modified on 19 Mar 2018


Published Paper

Inserted: 24 sep 2015
Last Updated: 19 mar 2018

Journal: Adv. Cal. Var.
Volume: 10
Pages: 183-207
Year: 2017
Doi: 10.1515/acv-2015-0036


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.