OSCILLATIONS AND CONCENTRATIONS GENERATED BY A-FREE MAPPINGS AND WEAK LOWER SEMICONTINUITY OF INTEGRAL FUNCTIONALS

@inproceedings{Fonseca2010OSCILLATIONSAC,
  title={OSCILLATIONS AND CONCENTRATIONS GENERATED BY A-FREE MAPPINGS AND WEAK LOWER SEMICONTINUITY OF INTEGRAL FUNCTIONALS},
  author={Irene Fonseca and Martin Kru{\vz}{\'i}k},
  year={2010}
}
DiPerna's and Majda's generalization of Young measures is used to describe oscillations and concentrations in sequences of maps {uk}k∈N ⊂ L p (Ω;R m ) satisfying a linear differential constraint Auk = 0. Applications to sequential weak lower semicontinuity of integral functionals on A-free sequences and to weak continuity of determinants are given. In particular, we state necessary and sufficient conditions for weak* convergence of det∇ϕk ∗ � det∇ϕ in measures on the closure of Ω ⊂ R n if ϕk… CONTINUE READING

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