Almost every level set of the viscosity solution to obstacle-constrained mean curvature flow is a distributional (BV) solution of the obstacle problem.
Mean curvature flow with obstacles: a viscosity approach
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abstract
We introduce a level-set formulation for the mean curvature flow with obstacles and show existence and uniqueness of a viscosity solution. These results generalize a well known viscosity approach for the mean curvature flow without obstacle by Evans and Spruck and Chen, Giga and Goto in 1991. In addition, we show that this evolution is consistent with the variational scheme introduced by Almeida, Chambolle and Novaga (2012) and we study the long time behavior of our viscosity solutions.
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Generic mean curvature flow with obstacles
Almost every level set of the viscosity solution to obstacle-constrained mean curvature flow is a distributional (BV) solution of the obstacle problem.