We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain Ω ⊂ ℝn. 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.
On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in ℝ2
FUSCO, GIORGIO;LEONETTI, Francesco;PIGNOTTI, CRISTINA
2017-01-01
Abstract
We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain Ω ⊂ ℝn. 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.File in questo prodotto:
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