Polygonal Hele?Shaw problem with surface tension

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. [5]. 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.