论文标题
一维brakke流的存在和规则定理
Existence and regularity theorems of one-dimensional Brakke flows
论文作者
论文摘要
鉴于$ \ Mathbb r^2 $的封闭式$ 1 $ -RECTIFIFIFIFIFIFIFIFIFIFIFIFFIFIFIFFIFFIFFFFF，我们证明存在从给定的集合开始，并具有以下规则性属性。几乎一直以来，该流程在本地由$ W^{2,2} $类的有限数量的嵌入曲线组成，其端点在交界处与0、60或120度的角度相交。
Given a closed countably $1$-rectifiable set in $\mathbb R^2$ with locally finite $1$-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 $W^{2,2}$ whose endpoints meet at junctions with angles of either 0, 60 or 120 degrees.
