Improved bounds for composites and rigidity of gradient fields

@article{Albin2007ImprovedBF,
  title={Improved bounds for composites and rigidity of gradient fields},
  author={Nathan Albin and S. Conti and V. Nesi},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2007},
  volume={463},
  pages={2031 - 2048}
}
  • Nathan Albin, S. Conti, V. Nesi
  • Published 2007
  • Mathematics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
We determine an improved lower bound for the conductivity of three-component composite materials. Our bound is strictly larger than the well-known Hashin–Shtrikman bound outside the regime where the latter is known to be optimal. The main ingredient of our result is a new quantitative rigidity estimate for gradient fields in two dimensions. 

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