$N\geq 2$维松弛Dirichlet问题的Wiener估计
A Wiener estimate for relaxed Dirichlet problems in dimension $N\geq 2$
摘要：
本文证明了松弛Dirichlet问题$Lu + μu =ν$在$Ω$中的Wiener能量估计，其中$L$是有界系数的一致椭圆算子，$μ$是${\cal M}_0(Ω)$的测度，$ν$是Kato测度，$Ω$是${\bf R}^N$，$N \geq 2$的有界开集.选择一个特殊的$μ$，我们得到了经典变分Dirichlet问题的能量估计.
英文摘要：
We prove a Wiener energy estimate for relaxed Dirichlet problems $Lu + μu =ν$ in $Ω$, with $L$ an uniformly elliptic operator with bounded coefficients, $μ$ a measure of ${\cal M}_0(Ω)$, $ν$ a Kato measure and $Ω$ a bounded open set of ${\bf R}^N$, $N \geq 2$. Choosing a particular $μ$, we obtain an energy estimate also for classical variational Dirichlet problems.
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