• DOI:10.1016/J.CRMA.2008.10.010
Corpus ID: 977784

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}
}

M. A. Pino, M. Kowalczyk, J. Wei

Published 2008

Mathematics

Comptes Rendus Mathematique

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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).