• Corpus ID: 222177152

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

@article{Bortz2020OptimalPK,
  title={Optimal Poisson kernel regularity for elliptic operators with H\"older-continuous coefficients in vanishing chord-arc domains},
  author={Simon Bortz and Tatiana Toro and Zihui Zhao},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
We show that if $\Omega$ is a vanishing chord-arc domain and $L$ is a divergence-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 the domain $\Omega$. This extends the previous work of Kenig and Toro in the case of the Laplacian. 
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