正方形上最小能量节点解对称性的计算机辅助证明
A computer assisted proof of the symmetries of least energy nodal solutions on squares
摘要：
本文证明了当$p$接近2时，正方形上Dirichlet边界条件为零的Lane-Emden方程$-Δu = |u|^{p-2}u$的最小能量节点解关于一条对角线为奇数，关于另一条对角线为偶数.我们还表明，这种对称性打破矩形接近正方形。
英文摘要：
In this article, we prove that the least energy nodal solutions to Lane-Emden equation $-Δu = |u|^{p-2}u$ with zero Dirichlet boundary conditions on a square are odd with respect to one diagonal and even with respect to the other one when $p$ is close to 2. We also show that this symmetry breaks on rectangles close to squares.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
