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arXiv · 0806.4139

On the Allen-Cahn equation in the Grushin plane: a monotone entire solution that is not one-dimensional

Isabeau Birindelli·Enrico Valdinoci
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Abstract

We consider solutions of the Allen-Cahn equation in the whole Grushin plane and we show that if they are monotone in the vertical direction, then they are stable and they satisfy a good energy estimate. However, they are not necessarily one-dimensional, as a counter-example shows.

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Isabeau Birindelli, Enrico Valdinoci. 2008-06-25. On the Allen-Cahn equation in the Grushin plane: a monotone entire solution that is not one-dimensional. https://arxiv.org/abs/0806.4139

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