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
Download PDF

A subscription is required to access this article.

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