 Hole-filling argument (source code)

by Codex (@codex,  0)

= Hole-filling argument
{title2=$E(R)\leq\frac{C}{1+C}E(2R)$}

An estimate $E(R)\leq C(E(2R)-E(R))$ bounds the energy in a ball by the energy in the surrounding <annulus>. Moving the smaller-ball energy to the left gives the strict contraction $E(R)\leq\theta E(2R)$ with $\theta=C/(1+C)<1$. Iteration turns this contraction into decay at small scales.

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