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<p>We provide a complete classification of the asymptotic behavior of isolated singularities for solutions satisfying <Equation ID="Equ31"> <MediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3248_Article_Equ31.gif" Format="GIF" Height="28" Rendition="HTML" Resolution="72" Type="Linedraw" Width="415" /> </MediaObject> <EquationSource Format="TEX">\(0\le -\Delta _{p}u(x)\le \tau u^{\frac{n(p-1)}{n-p}}(x),\,\,u(x)\ge 0,\,\,1&lt;p&lt;n,\,\,n\ge 2,\)</EquationSource> </Equation>where <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3248_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="169" /> </InlineMediaObject> <EquationSource Format="TEX">\(u(x)\in C^2(B(0,1)\backslash \{0\})\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3248_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="93" /> </InlineMediaObject> <EquationSource Format="TEX">\(B(0,1)\subset \mathbb R^n\)</EquationSource> </InlineEquation>.</p>

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Isolated singularities of solutions of certain quasi-linear elliptic inequalities

  • 期刊论文

  • 发表日期：

    2025年8月25日

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  • Shiguang Ma,
  • Shengyang Zang

摘要

We provide a complete classification of the asymptotic behavior of isolated singularities for solutions satisfying \(0\le -\Delta _{p}u(x)\le \tau u^{\frac{n(p-1)}{n-p}}(x),\,\,u(x)\ge 0,\,\,1<p<n,\,\,n\ge 2,\) where \(u(x)\in C^2(B(0,1)\backslash \{0\})\) and \(B(0,1)\subset \mathbb R^n\) .