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Forced symmetry-breaking via boundary conditions

Zhen Mei·Chih-Wen Shih
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Abstract

We study impact of a forced symmetry-breaking in boundary conditions on the bifurcation scenario of a semilinear elliptic partial differential equation. We show that for the square domain the orthogonality of eigenfunctions of the Laplacian may compensate partially the loss of symmetries in the boundary conditions and allows some solution to have more symmetries than the imposed boundary conditions.

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Zhen Mei, Chih-Wen Shih. 1998-04-14. Forced symmetry-breaking via boundary conditions. https://arxiv.org/abs/math/9804160

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