46 citations · 221 across the 21 of their papers we have counts for
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Existence and regularity theorems of one-dimensional Brakke flows
Lami Kim, Yoshihiro Tonegawa
Given a closed countably -rectifiable set in with locally finite -dimensional Hausdorff measure, we prove that there exists a Brakke flow starting from the give…
On the mean curvature flow of grain boundaries
Lami Kim, Yoshihiro Tonegawa
Suppose that is a closed countably -rectifiable set whose complement consists of more than one connected component. As…
Existence and regularity of mean curvature flow with transport term in higher dimensions
Keisuke Takasao, Yoshihiro Tonegawa
Given an initial hypersurface and a time-dependent vector field in a Sobolev space, we prove a time-global existence of a family of hypersurfaces which start from the given h…
Stable phase interfaces in the van der Waals--Cahn--Hilliard theory
Yoshihiro Tonegawa, Neshan Wickramasekera
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals--Cahn--Hilliard energ…