Integrality of varifolds in the singular limit of reaction-diffusion equations
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概要
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We answer a question posed by Ilmanen on the integrality of varifolds which appear as the singularperturbation limit of the Allen-Cahn equation. We show that the density of the limit measure isinteger multiple of the surface constant almost everywhere at almostall time. This shows that limit measures obtained via the Allen-Chanequation and those via Brakke's construction share the same integralityproperty as well as being weak solutions for the mean curvature flow equation.
- 広島大学の論文
著者
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利根川 吉広
北海道大学理学院
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Tonegawa Yoshihiro
Department Of Mathematics Hokkaido University
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Tonegawa Yoshihiro
Department Of Mathematics Faculty Of Science Hokkaido University
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