论文标题
小型$ a_ \ infty $ $ dahlberg-kenig-pipher operators的套装，均匀校正边界
Small $A_\infty$ results for Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries
论文作者
论文摘要
In the present paper, we consider elliptic operators $L=-\textrm{div}(A\nabla)$ 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与$ l $相关的无穷大的极是$ a_ \ infty $ - 在$γ$上的表面度量方面绝对连续，带有小$ a_ \ infty $常数。换句话说，我们表明，对于相对平坦的均匀校正组合，对于具有缓慢振荡系数的操作员，椭圆措施满足$ a_ \ infty $条件，其常数较小，而泊松仁的对数具有较小的振荡。
In the present paper, we consider elliptic operators $L=-\textrm{div}(A\nabla)$ 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 $A_\infty$-absolutely continuous with respect to the surface measure on $Γ$, with a small $A_\infty$ 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 $A_\infty$ condition with a small constant and the logarithm of the Poisson kernel has small oscillations.
