论文标题
$ l^p $估算近乎奇异性和bôcher型定理的正谐波功能的估计值
$L^p$ estimate for positive harmonic functions near singularities and Bôcher type theorems
论文作者
论文摘要
在本文中，研究了具有一维圆形奇点的拉普拉斯方程的阳性解决方案。首先，与经典$ l^1 $估计相比，我们建立了此类解决方案$ U $的$ l^p $集成性估算。然后，我们在圆圈周围表征$-ΔU$。我们开发的方法也可以适应更高的维度和更广泛的病例。
In this paper, positive solutions to the Laplace equation with 1-dimensional circular singularities are investigated. First, we establish $L^p$ integrability estimates for such solutions $u$ near the singularities, in comparison with classical $L^1$ estimates. Then we characterize $-Δu$ around the circle. The method we developed may also be adapted to higher dimensional as well as more generalized cases.
