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arXiv · 2611.03483

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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Shiguang Ma, Shengyang Zang. 2026-11-02. Sharp bounds and asymptotic profiles for Lane-Emden systems at the Serrin threshold. https://arxiv.org/abs/2611.03483

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