# A counterexample to a conjecture by De Giorgi in large dimensions

```@article{Pino2008ACT,
title={A counterexample to a conjecture by De Giorgi in large dimensions},
author={M. A. Pino and M. Kowalczyk and J. Wei},
journal={Comptes Rendus Mathematique},
year={2008},
volume={346},
pages={1261-1266}
}```
• Published 2008
• Mathematics
• Comptes Rendus Mathematique
• We consider the Allen–Cahn equation Δu+u(1−u2)=0in RN. A celebrated conjecture by E. De Giorgi (1978) states that if u is a bounded solution to this problem such that ∂xNu>0, then the level sets {u=λ}, λ∈R, must be hyperplanes at least if N⩽8. We construct a family of solutions which shows that this statement does not hold true for N⩾9. To cite this article: M. del Pino et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).
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