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arXiv · 2102.07596

A computer assisted proof of the symmetries of least energy nodal solutions on squares

Ariel Salort·Christophe Troestler
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Abstract

In this article, we prove that the least energy nodal solutions to Lane-Emden equation $-{\Delta}u = |u|^{p-2}u$ 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.

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Ariel Salort, Christophe Troestler. 2021-02-15. A computer assisted proof of the symmetries of least energy nodal solutions on squares. https://arxiv.org/abs/2102.07596

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