JournalsifbVol. 22, No. 4pp. 505–550

Existence and regularity theorems of one-dimensional Brakke flows

  • Lami Kim

    Yonsei University, Seoul, Republic of Korea
  • Yoshihiro Tonegawa

    Tokyo Institute of Technology, Japan
Existence and regularity theorems of one-dimensional Brakke flows cover
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Abstract

Given a closed countably 1-rectifiable set in R2\mathbb R^2 with locally finite 11-dimensional Hausdorff measure, we prove that there exists a Brakke flow starting from the given set with the following regularity property. For almost all time, the flow locally consists of a finite number of embedded curves of class~W2,2W^{2,2} whose endpoints meet at junctions with angles of either 0, 60 or 120 degrees.

Cite this article

Lami Kim, Yoshihiro Tonegawa, Existence and regularity theorems of one-dimensional Brakke flows. Interfaces Free Bound. 22 (2020), no. 4, pp. 505–550

DOI 10.4171/IFB/448