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

Shuimu Li

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

Analysis of PDEs 2022-03-08 v1

Authors: Shuimu Li

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.

Keywords

positive harmonic functions laplace equation circular singularities l^p estimate bôcher theorem

Cite

@article{arxiv.2203.03219,
  title  = {$L^p$ estimate for positive harmonic functions near singularities and B\^{o}cher type theorems},
  author = {Shuimu Li},
  journal= {arXiv preprint arXiv:2203.03219},
  year   = {2022}
}

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