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arXiv · 2203.03219

$L^p$ estimate for positive harmonic functions near singularities and B\^{o}cher type theorems

Shuimu Li
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Abstract

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 $-\Delta u$ around the circle. The method we developed may also be adapted to higher dimensional as well as more generalized cases.

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Shuimu Li. 2022-03-07. $L^p$ estimate for positive harmonic functions near singularities and B\^{o}cher type theorems. https://arxiv.org/abs/2203.03219

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