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 with locally finite -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 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