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PreprintCC BY 4.0arXiv

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 C1,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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Cite

BibTeXRIS
BibTeX
@misc{ma2026isolated,
  title = {{Isolated singularities of certain quasi-linear elliptic inequalities II}},
  author = {Shiguang Ma and Shengyang Zang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29113},
  eprint = {2610.29113},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29113},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Isolated singularities of certain quasi-linear elliptic inequalities II
AU  - Shiguang Ma
AU  - Shengyang Zang
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29113
UR  - https://arxiv.org/abs/2610.29113
AB  - 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.
ER  -