On Obstacle Problem for Brakke's Mean Curvature Flow
On Obstacle Problem for Brakke's Mean Curvature Flow
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DOI：
10.1137/21m1400432
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
K. Takasao
中科院分区：
文献类型：
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作者：
K. Takasao
在Brakke平均曲率流意义下，我们考虑了平均曲率流弱解的障碍问题。证明了二维和三维空间中具有$C^{1，1}$边界的障碍弱解的整体存在性。为了得到弱解，我们使用了带强迫项的Allen-Cahn方程。
We consider the obstacle problem of the weak solution for the mean curvature flow, in the sense of Brakke's mean curvature flow. We prove the global existence of the weak solution with obstacles which have $C^{1,1}$ boundaries, in two and three space dimensions. To obtain the weak solution, we use the Allen-Cahn equation with forcing term.