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We show that if $\Omega$ is a vanishing chord-arc domain and $L$ is adivergence-form elliptic operator with H\"older-continuous coefficient matrix,then $\log k_L \in VMO$, where $k_L$ is the elliptic kernel for $L$ in thedomain $\Omega$. This extends the previous work of Kenig and Toro in the caseof the Laplacian.

Optimal Poisson kernel regularity for elliptic operators with H\"older-continuous coefficients in vanishing chord-arc domains