Optimal Poisson kernel regularity for elliptic operators with Holder continuous coefficients in vanishing chord-arc domains

We show that if 12 is a vanishing chord-arc domain and L is a divergence-form elliptic operator with Holder-continuous coefficient matrix, then log kL & ISIN; VMO, where kL is the elliptic Poisson kernel for L in the domain 12. This extends the previous work of Kenig and Toro in the case of the Laplacian. & COPY; 2023 Elsevier Inc. All rights reserved.