Abstract

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.

Author information

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

Mikhail A. Sychev

Sobolev Institute for Mathematics, Koptuyg Avenue 4, Novosibirsk 630090, Russia

masychev@math.nsc.ru

Keywords

  • Integral functionals
  • lower semicontinuity
  • relaxation
  • mathematical theory of elasticity
  • strong materials

Mathematics Subject Classification

35F30, 35J55, 49K20, 73G05

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Suggested citation

M. A. Sychev. “First General Lower Semicontinuity and Relaxation Results for Strong Materials.” Journal of Convex Analysis 17 (2010), No. 1, 183–202. https://doi.org/10.68381/jca17014

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.