We give a simple proof that the solution of the Allen-Cahn equation converges to Brakke's motion by mean curvature, by utilizing the recent results of Röger and Schätzle in space dimension 2 and 3.
Abstract. Let D = ℍ \ ⋃ k = 1 N C k be a standard slit domain where ℍ is the upper half-plane and Ck, 1 ≤ k ≤ N, are mutually disjoint horizontal line segments in ℍ. Given a Jordan arc γ ⊂ D starting ...
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