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Sharp bounds and asymptotic profiles for Lane-Emden systems at the Serrin threshold

  • Shiguang Ma
  • Shengyang Zang
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Abstract

We classify isolated singularities of p-Laplace and k-Hessian Lane--Emden systems on their Serrin critical curves without radial symmetry. Our approach reconstructs a radial profile from the source measures through a truncated Wolff potential, providing a nonlinear counterpart of spherical averaging. For upper inequalities at equal powers, we determine the sharp joint logarithmic lower bound on the zero-mass singular branch. A radial pair attains this bound while both normalized components oscillate between zero and infinity. For exact systems at equal powers, we obtain a common second-order profile with a shared phase and a sharp two-term logarithmic expansion of the component difference. At unequal powers, we establish power--logarithmic asymptotics with explicit leading constants. These asymptotics hold uniformly in direction.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026sharp,
  title = {{Sharp bounds and asymptotic profiles for Lane-Emden systems at the Serrin threshold}},
  author = {Shiguang Ma and Shengyang Zang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03483},
  eprint = {2611.03483},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03483},
}
RIS
TY  - UNPB
TI  - Sharp bounds and asymptotic profiles for Lane-Emden systems at the Serrin threshold
AU  - Shiguang Ma
AU  - Shengyang Zang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03483
UR  - https://arxiv.org/abs/2611.03483
AB  - We classify isolated singularities of p-Laplace and k-Hessian Lane--Emden systems on their Serrin critical curves without radial symmetry. Our approach reconstructs a radial profile from the source measures through a truncated Wolff potential, providing a nonlinear counterpart of spherical averaging. For upper inequalities at equal powers, we determine the sharp joint logarithmic lower bound on the zero-mass singular branch. A radial pair attains this bound while both normalized components oscillate between zero and infinity. For exact systems at equal powers, we obtain a common second-order profile with a shared phase and a sharp two-term logarithmic expansion of the component difference. At unequal powers, we establish power--logarithmic asymptotics with explicit leading constants. These asymptotics hold uniformly in direction.
ER  -