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

Giorgio Fusco, Francesco Leonetti, Cristina Pignotti

We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain $\Omega \subset {\mathbf{R}}^n.$ Under suitable assumptions, we prove an existence result…