Improved bounds for composites and rigidity of gradient fields
Nathan Albin, Sergio Conti, Vincenzo Nesi · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2007
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.