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arXiv · 2404.03763

On an obstacle problem for the Brakke flow with a generalized right-angle boundary condition

Katerina Nik·Keisuke Takasao
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Abstract

We study Brakke's mean curvature flow with obstacles and with a right-angle boundary condition. Assuming that the obstacles have $C^{1,1}$-boundaries we prove that a weak solution exists globally in time. To show the existence we apply the phase-field method and thus investigate the singular limit of the Allen-Cahn equation with forcing term and homogeneous Neumann bounday condition. We also construct sub- and supersolutions that correspond to the obstacles.

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Katerina Nik, Keisuke Takasao. 2024-04-04. On an obstacle problem for the Brakke flow with a generalized right-angle boundary condition. https://arxiv.org/abs/2404.03763

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