Removable singularity of the polyharmonic equation

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dc.creatorHsu, Shu-Yu
dc.date2007-02-07
dc.date.accessioned2026-07-07T07:45:19Z
dc.date.available2026-07-07T07:45:19Z
dc.descriptionLet $x_0\inΩ\subset\Bbb{R}^n$, $n\ge 2$, be a domain and let $m\ge 2$. We will prove that a solution $u$ of the polyharmonic equation $Δ^mu=0$ in $Ω\setminus\{x_0\}$ has a removable singularity at $x_0$ if and only if $|Δ^ku(x)|=o(|x-x_0|^{2-n})\quad\forall k=0,1,2,...,m-1$ as $|x-x_0|\to 0$ for $n\ge 3$ and $=o(\log (|x-x_0|^{-1}))\quad\forall k=0,1,2,...,m-1$ as $|x-x_0|\to 0$ for $n=2$. For $m\ge 2$ we will also prove that $u$ has a removable singularity at $x_0$ if $|u(x)|=o(|x-x_0|^{2m-n})$ as $|x-x_0|\to 0$ for $n\ge 3$ and $|u(x)| =o(|x-x_0|^{2m-2}\log (|x-x_0|^{-1}))$ as $|x-x_0|\to 0$ for $n=2$.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0702171
dc.identifierhttp://arxiv.org/abs/math/0702171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123494
dc.subjectAnalysis of PDEs
dc.subject35B65, 35J30, 35J99
dc.titleRemovable singularity of the polyharmonic equation
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