Abstract

A lower semicontinuity result is proved in the space of special functions of bounded deformation for a fracture energetic model according to Barenblatt's theory, i.e. ∫Juφ([u]⋅νu)dHN−1,[u]⋅νu≥0HN−1− a.e. on Ju.\int_{J_{u}} \varphi([u] \cdot \nu_{u})d {\cal H}^{N-1} \enspace, \enspace [u]\cdot \nu_u \geq 0 \enspace {\cal H}^{N-1} - \hbox{ a.e. on }J_u.

Author information

Contact details are reproduced from the original publication and may be historical.

Giuliano Gargiulo

Dip. di Scienze Biologiche ed Ambientali, Università degli Studi del Sannio, Via Port'Arsa, 82100 Benevento, Italy

giuliano.gargiulo@unisannio.it

Elvira Zappale

Dip. di Ingegneria dell'Informazione e Matematica Applicata, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

zappale@diima.unisa.it

Keywords

  • Lower semicontinuity
  • fracture
  • special functions of bounded deformation
  • convexity
  • subadditivity

Mathematics Subject Classification

49J45, 26B25, 26B30, 26D10, 39B62, 74A45, 74B20, 74R99

Suggested citation

G. Gargiulo, E. Zappale. “A Lower Semicontinuity Result in SBD.” Journal of Convex Analysis 15 (2008), No. 1, 191–200.

Copyright Heldermann Verlag 2008