# 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}
}
• 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.

#### References

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