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Remarks on convergence of the Allen-Cahn equation
| Title: | Remarks on convergence of the Allen-Cahn equation |
| Authors: | Tonegawa, Y. Browse this author |
| Issue Date: | Jun-2001 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 531 |
| Start Page: | 1 |
| End Page: | 18 |
| Abstract: | We answer a question posed by Ilmanen on the integrality of varifolds which appear as the singular perturbation limit of the Allen-Cahn equation. We show that the density of the limit measure is integer multiple of the surface constant 1-1,n-1-a.e. for a.e. time. This shows that limit measures obtained via the AllenCahn equation and those via Brakke's construction share the same integrality property as well as being weak solutions for the mean curvature flow equation. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69281 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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