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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/148433
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