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

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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

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Suggested citation

G. Gargiulo, E. Zappale. “A Lower Semicontinuity Result in SBD.” Journal of Convex Analysis 15 (2008), No. 1, 191–200. https://doi.org/10.68381/jca15013

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.