= Taylor normalization in elliptic blow-up arguments
{c}
{title2=$v(z)=\frac{u(x+rz)-T_x^2u(x+rz)}{Ar^{2+\mu}}$}
Subtracting the quadratic <Taylor polynomial> at the rescaling centre makes the function, <gradient> and <Hessian matrix> vanish there. Dividing by $Ar^{2+\mu}$ preserves the normalized Hölder oscillation of the <Hessian matrix> while turning a small forcing-to-oscillation ratio into a harmonic limiting equation. The three vanished Taylor coefficients provide local bounds needed by the <Arzelà-Ascoli theorem>.
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