## Abstract

In the present paper we consider elliptic operators L = − div(A∇) in a domain bounded by a chord-arc surface Γ with small enough constant, and whose coefficients A satisfy a weak form of the Dahlberg-Kenig-Pipher condition of approximation by constant coefficient matrices, with a small enough Carleson norm, and show that the elliptic measure with pole at infinity associated to L is A∞-absolutely continuous with respect to the surface measure on Γ, with a small A∞ constant. In other words, we show that for relatively flat uniformly rectifiable sets and for operators with slowly oscillating coefficients the elliptic measure satisfies the A∞ condition with a small constant and the logarithm of the Poisson kernel has small oscillations.

Original language | English (US) |
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Pages (from-to) | 7857-7909 |

Number of pages | 53 |

Journal | Transactions of the American Mathematical Society |

Volume | 376 |

Issue number | 11 |

DOIs | |

State | Published - 2023 |

### Bibliographical note

Publisher Copyright:C 2023 American Mathematical Society.

## Keywords

- A∞
- Elliptic measure
- small constants
- uniform rectiability
- weak Dahlberg-Kenig-Pipher condition

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