Calculus of Variations and Geometric Measure Theory

G. P. Leonardi

Partitions with prescribed mean curvatures

created on 18 Sep 2001
modified on 10 Dec 2002


Published Paper

Inserted: 18 sep 2001
Last Updated: 10 dec 2002

Journal: Manuscripta Math.
Volume: 107
Number: 1
Pages: 111-133
Year: 2002


We consider a certain variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation, and generalizes the well-known problem with prescribed mean curvature. We prove existence and regularity results, and finally show some explicit examples of minimizers.

Keywords: Immiscible fluids, Image segmentation, Caccioppoli partitions