BMO Solvability and A ∞ Condition of the Elliptic Measures in Uniform Domains

BMO Solvability and A ∞ Condition of the Elliptic Measures in Uniform Domains
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均匀域椭圆测度的BMO可解性和A ∞ 条件

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发表时间：
2017
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通讯作者：
Zihui Zhao
Zihui Zhao
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作者：
Zihui Zhao

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考虑系数有界可测椭圆算子散度的Dirichlet边值问题。证明了对于具有Ahlfors正则边界的一致域，这类问题的BMO可解性等价于椭圆测度相对于曲面测度的定量绝对连续性，即
We consider the Dirichlet boundary value problem for divergence form elliptic operators with bounded measurable coefficients. We prove that for uniform domains with Ahlfors regular boundary, the BMO solvability of such problems is equivalent to a quantitative absolute continuity of the elliptic measure with respect to the surface measure, i.e