Taylor normalization in elliptic blow-up arguments
ID: taylor-normalization-in-elliptic-blow-up-arguments
Subtracting the quadratic Taylor polynomial at the rescaling centre makes the function, gradient and Hessian matrix vanish there. Dividing by 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 Arzela-Ascoli theorem.
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