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Journal of Convex Analysis 17 (2010), No. 1, 183--202
Copyright Heldermann Verlag 2010

First General Lower Semicontinuity and Relaxation Results for Strong Materials

Mikhail A. Sychev
Sobolev Institute for Mathematics, Koptuyg Avenue 4, Novosibirsk 630090, Russia

We consider the case of strong materials, i.e. the situation where the growth of integrands from below guarantees the lack of discontinuities for deformations with finite energy. We show that, in this case, both lower semicontinuity and relaxation results relay on the a.e. differentiability property of admissible deformations and on the uniform convergence of weakly convergent sequences bounded in energy.

Keywords: Integral functionals, lower semicontinuity, relaxation, mathematical theory of elasticity, strong materials.

MSC: 35F30, 35J55, 49K20, 73G05

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