Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 47, Issue 3, Pages 1906-1932Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140987808
Keywords
boundary monotonicity formula; Allen-Cahn equation; mean curvature flow; varifold
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Funding
- JSPS KAKENHI [21224001, 25800084, 25247008]
- Grants-in-Aid for Scientific Research [25800084, 21224001, 25247008] Funding Source: KAKEN
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We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.
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