Sala Seminari (Dip. Matematica).<\/p>\n
We consider in the plane a fixed finite number N of “bubbles”, that is disjoint finite perimeter sets which possibly share portions of their boundaries, and look for configurations that minimize, under a volume constraint, the total weighted length of their boundaries: the interface between each bubble and the exterior is given weight 1 while the interface between any two bubbles is given weight $2-\\varepsilon$. We are interested in the case when $\\epsilon$ converges to 0: we prove that minimizing configurations approach in the limit a configuration of disjoint disks which maximize the number of tangencies among them. Moreover we obtain some information about the structure of minimizers for small $\\varepsilon$.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider in the plane a fixed finite number N of “bubbles”, that is disjoint finite perimeter sets which possibly share portions of their boundaries, and look for configurations that minimize, under a volume constraint, the total weighted length…<\/p>\n