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

Gianni Dal Masohttp://orcid.org/0000-0002-1010-4968 1 , Gianluca Orlando 2 , and Rodica Toader 3
  • 1 SISSA, Via Bonomea 265, 34136 Trieste, Italy
  • 2 SISSA, Via Bonomea 265, 34136 Trieste, Italy
  • 3 DIMA, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy
Gianni Dal MasoORCID iD: http://orcid.org/0000-0002-1010-4968, Gianluca Orlando and Rodica Toader

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 L1 convergence.

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