Partitions with prescribed mean curvatures (Q1598170)

The author considers a variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation. The functional introduced by the author generalizes a previous one discussed by \textit{U. Massari} [Arch. Ration. Mech. Anal. 55, 357-382 (1974; Zbl 0305.49047); Rend. Sem. Mat. Univ. Padova 53(1975), 37-52 (1976; Zbl 0358.49019)] in connection with the study of sets with prescribed mean curvature. The paper provides existence as well as regularity results, moreover, some interesting examples are presented.