Liftings, Young Measures, and Lower Semicontinuity

@article{Rindler2018LiftingsYM,
  title={Liftings, Young Measures, and Lower Semicontinuity},
  author={Filip Rindler and Giles Shaw},
  journal={Archive for Rational Mechanics and Analysis},
  year={2018},
  volume={232},
  pages={1227-1328}
}
  • F. Rindler, Giles Shaw
  • Published 14 August 2017
  • Mathematics
  • Archive for Rational Mechanics and Analysis
AbstractThis work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs (uj, Duj)j for $${(u_j)_j\subset {\rm BV}(\Omega;\mathbb{R}^m)}$$(uj)j⊂BV(Ω;Rm) under weak* convergence. These tools are then used to prove an integral representation theorem for the relaxation of the functional $$\mathcal{F}\colon u\mapsto\int_\Omega f(x,u(x),\nabla u(x))\, {\rm d}x, \quad u \in {\rm W}^{1,1}(\Omega;\mathbb{R}^m),\quad\Omega\subset… 
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