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

Abstract

We show that if Ω is a vanishing chord-arc domain and L is a divergence-form elliptic operator with Hölder-continuous coefficient matrix, then log⁡kL∈VMO, where kL is the elliptic Poisson kernel for L in the domain Ω. This extends the previous work of Kenig and Toro in the case of the Laplacian.