Definition of the Brakke Flow

  • Yoshihiro Tonegawa
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


Suppose that we have a family of smooth surfaces {Γ(t)}t ∈ [0,T) for some T ≤ with no boundaries in \(U\subset \mathbb {R}^n\). Let v = v(Γ(t), x) be the normal velocity vector of Γ(t) at x ∈ Γ(t). Here we consider how one may characterize the normal velocity using integration. The reason for such a pursuit is that, in the end, we want to replace Γ(t) by a general varifold. To do so, let \(\phi \in C_c^1(U\times [0,T);\mathbb {R}^+)\) be a non-negative “test function”.


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Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yoshihiro Tonegawa
    • 1
  1. 1.Tokyo Institute of TechnologyTokyoJapan

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