Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Ma, Shiguang, Zang, Shengyang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225194280