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Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional
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- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.30194
- Original
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Abstract
We prove that every bounded stable solution of the Allen--Cahn equation in $\mathbb R^3$ is one-dimensional. As a consequence, this shows the validity of De Giorgi's conjecture for monotone solutions in dimension four.
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