A fourth-order regularization of the curvature flow of immersed plane curves with Dirichlet boundary conditions
Abstract
We consider a fourth-order regularization of the curvature flow for an immersed plane curve with fixed boundary, using an elastica-type functional depending on a small positive parameter . We show that the approximating flow smoothly converges, as 0+, to the curvature flow of the curve with Dirichlet boundary conditions for all times before the first singularity of the limit flow.
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