论文标题
Cantor套装上的好椭圆运算符
Good elliptic operators on Cantor sets
论文作者
论文摘要
众所周知，纯粹的不可分割的集合无法支持与此集合的Hausdorff度量绝对连续的谐波度量。我们表明，在$ {\ mathbb {r}}^2 $中，（纯粹是不可分割的）cantor设置的椭圆操作员仍然存在椭圆机，其椭圆度绝对是连续的，实际上与Hausdorff措施成正比。
It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that nonetheless there exist elliptic operators on (purely unrectifiable) Cantor sets in ${\mathbb{R}}^2$ whose elliptic measure is absolutely continuous, and in fact, essentially proportional to the Hausdorff measure.
