Local Approximation of $A$-Harmonic Functions and the Super-Localization Conjecture

We consider the local energy approximation of $A$-harmonic functions on concentric cubes with a fixed size ratio in $\mathbb{R}^d$, $d\ge2$, for bounded, symmetric, uniformly elliptic diffusion tensors~$A$. We give a short proof of the Kolmogorov $n$-width decay rate $\exp(-cn^{1/(d-1)})$ conjecture