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November 2003 Integrality of varifolds in the singular limit of reaction-diffusion equations
Yoshihiro Tonegawa
Hiroshima Math. J. 33(3): 323-341 (November 2003). DOI: 10.32917/hmj/1150997978

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 almost everywhere at almost all time. This shows that limit measures obtained via the Allen- Chan equation and those via Brakke’s construction share the same integrality property as well as being weak solutions for the mean curvature flow equation.

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Yoshihiro Tonegawa. "Integrality of varifolds in the singular limit of reaction-diffusion equations." Hiroshima Math. J. 33 (3) 323 - 341, November 2003. https://doi.org/10.32917/hmj/1150997978

Information

Published: November 2003
First available in Project Euclid: 22 June 2006

zbMATH: 1059.35061
MathSciNet: MR2040901
Digital Object Identifier: 10.32917/hmj/1150997978

Subjects:
Primary: 35K57
Secondary: 35B25, 49Q20, 53C44

Rights: Copyright © 2003 Hiroshima University, Mathematics Program

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Vol.33 • No. 3 • November 2003
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