On the mean curvature flow of grain boundaries
By Lami Kim, Yoshihiro Tonegawa. 2015
58 citations recorded by the source corpus.
Suppose that $\Gamma_0\subset\mathbb R^{n+1}$ is a closed countably $n$-rectifiable set whose complement $\mathbb R^{n+1}\setminus \Gamma_0$ consists of more than one connected component. Assume that the $n$-dimensional Hausdorff measure of $\Gamma_0$ is finite or grows at most exponentially near infinity. Under these assumptions, we prove a global-in-time existence of mean curvature flow in the sense of Brakke starting from $\Gamma_0$. There exists a finite family of open sets which move continuously with respect to the Lebesgue measure, and whose boundaries coincide with the space-time support of the mean curvature flow.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bdc4196c2609484286363e114a373a3daa47a058
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Tim Laux
- Felix Otto
- Cédric Villani
- José Antonio Carrillo
- J. Lott
- Luigi Ambrosio
- S. Armstrong
- Jean-Christophe Mourrat
In Mathematical Physics
Citations in the corpus
- Convergence of the thresholding scheme for multi-phase mean-curvature flow (2016, background): “Recently, Kim and Tonegawa [21] improved this work by deriving the continuity of the volumes of the grains in the case of grain growth with equal surface tensions which ensures that the solution is non-trivial.”