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Journal of Convex Analysis 15 (2008), No. 1, 191--200
Copyright Heldermann Verlag 2008

A Lower Semicontinuity Result in SBD

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

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


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. $$\int_{J_{u}} \varphi([u] \cdot \nu_{u})d {\cal H}^{N-1} \enspace, \enspace [u]\cdot \nu_u \geq 0 \enspace {\cal H}^{N-1} - \hbox{ a.e. on }J_u.$$

Keywords: Lower semicontinuity, fracture, special functions of bounded deformation, convexity, subadditivity.

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

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