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arXiv · 1405.1541

On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in ${\bf R}^2$

Giorgio Fusco·Francesco Leonetti·Cristina Pignotti
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Abstract

We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain $Ω\subset {\bf R}^n.$ Under suitable assumptions, we prove an existence result and a uniform exponential estimate for symmetric solutions. In dimension n=2 an additional asymptotic result is obtained. These results are based on a pointwise estimate obtained for local minimizers of the Allen-Cahn energy.

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Giorgio Fusco, Francesco Leonetti, Cristina Pignotti. 2014-05-07. On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in ${\bf R}^2$. https://arxiv.org/abs/1405.1541

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