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arXiv · 2610.29113

Isolated singularities of certain quasi-linear elliptic inequalities II

Shiguang Ma·Shengyang Zang
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Abstract

In this paper, we study the asymptotic behavior of isolated singularities for quasilinear elliptic equations of $p$-Laplacian type. We focus on the $p$-Laplace equation with the critical Serrin exponent $n(p-1)/(n-p)$ and the $n$-Laplace equation with critical exponential growth. We prove that any positive solution either admits a $C^{1,α}$ extension to the origin or exhibits a precise singular asymptotic behavior. These results provide a complement to our previous study on $p$-Laplacian type inequalities.

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Shiguang Ma, Shengyang Zang. 2026-10-21. Isolated singularities of certain quasi-linear elliptic inequalities II. https://arxiv.org/abs/2610.29113

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