Integrality of varifolds in the singular limit of reaction-diffusion equations
Tonegawa, Yoshihiro
Hiroshima Math. J., Tome 33 (2003) no. 1, p. 323-341 / Harvested from Project Euclid
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/