Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems of Fracture Mechanics

Details Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems of Fracture Mechanics Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems of Fracture Mechanics

2009-12-28

arxiv.org/abs/0912.5131v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

We provide some lower semicontinuity results in the space of special functions of bounded deformation for energies of the type $$ %\int_\O {1/2}({\mathbb C} \E u, \E u)dx + \int_{J_{u}} \Theta(u^+, u^-, \nu_{u})d \H^{N-1} \enspace, \enspace [u]\cdot \nu_u \geq 0 \enspace {\cal H}^{N-1}-\hbox{a. e. on}J_u, $$ and give some examples and applications to minimum problems. \noindent Keywords: Lower semicontinuity, fracture, special functions of bounded deformation, joint convexity, $BV$-ellipticity.

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