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| Earlier, we constructed variational solutions for closed curves driven by a singular wmc flow. Actually, we considered curves which are small perturbations of a scaled Wulff shape, i.e. a ball in the norm specified by the anisotropy function.
Recently, M.-H.Giga and Y.Giga have developed the viscosity theory for singular parabolic problems in one-dimension. In order to make this theory work, we treat our evolving curve as graph over a suitable reference manifold and we rewrite the wmc flow as a singular parabolic pde for an evolving graph.
Using the methods of the viscosity theory we study issues, which were not tractable with the tools we used earlier. In particular, we show uniqueness of solutions and address the corner persistence problem. |
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