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.
Publié le : 2003-11-14
Classification:
35K57,
35B25,
49Q20,
53C44
@article{1150997978,
author = {Tonegawa, Yoshihiro},
title = {Integrality of varifolds in the singular limit of reaction-diffusion equations},
journal = {Hiroshima Math. J.},
volume = {33},
number = {1},
year = {2003},
pages = { 323-341},
language = {en},
url = {http://dml.mathdoc.fr/item/1150997978}
}
Tonegawa, Yoshihiro. Integrality of varifolds in the singular limit of reaction-diffusion equations. Hiroshima Math. J., Tome 33 (2003) no. 1, pp. 323-341. http://gdmltest.u-ga.fr/item/1150997978/