临界勒贝格空间中带反对称势的n-Laplace系统的非正则性
Non-Regularizing properties of $n$-Laplace systems with antisymmetric potentials in critical Lebesgue spaces
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中文总结 AI 辅助
该研究针对n≥3的情况构造了带反对称势的n-Laplace系统的有界不连续解，证明了相关正则性结果的最优性，否定了Rivière的问题。
中文摘要 AI 辅助
对于每个n≥3，我们构造了一个有界不连续映射u∈W^{1,n}(Bⁿ,ℝ^{n+2})，求解带反对称势Ω∈Lⁿ的n-Laplace系统。这表明，作者近期关于洛伦兹空间中带反对称势的n-Laplace系统的正则性结果是最优的，即无法从洛伦兹空间过渡到经典勒贝格空间，尤其对Rivière提出的问题给出了否定答案。
英文摘要
For every $n\geq 3$ we construct a bounded discontinuous map $u\in W^{1,n}(\mathbb{B}^n,\mathbb{R}^{n+2})$ solving an $n$-Laplace system with an antisymmetric potential $Ω\in L^n$. This shows that a recent regularity result on $n$-Laplace systems with antisymmetric potentials in Lorentz spaces by the authors is sharp in the sense that we cannot move from Lorentz spaces to classical Lebesgue spaces. This gives in particular a negative answer to a question by Rivière.
