Asymptotic planar N-bubble

Wednesday, November 22, 2017
Giacomo Del Nin
Universita' di Pisa
Abstract. 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 $\varepsilon$.