We study a polygonal analogue of the Hele?Shaw moving boundary problem with surface tension based on a framework of polygonal motion proposed by Bene¡s et al. . A key idea is to introduce a polygonal Dirichlet-to-Neumann map. We study variational properties of the polygonal Dirichletto-Neumann map and show that our polygonal Hele?Shaw problem is a polygonal analogue of the original problem. Local solvability of a polygonal Hele?Shaw problem is also proved by means of the variational structure.
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