Gamma-convergence for one-dimensional nonlocal phase transition energies
Abstract
We study the asymptotic behavior as ε goes to 0 of an appropriate scaling of the following nonlocal Allen-Cahn energy,
where I is an interval in R, and W is a double-well potential. We provide a Γ-convergence result for any s ∈ (0,1), by extending the case when s=1/2 studied by Alberti, Bouchittè and Seppecher in [2]. We also investigate the convergence as s↗1 of the related optimal profile problem to the local counterpart.
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