Calculus of Variations and Geometric Measure Theory

G. P. Leonardi - I. Tamanini

Metric spaces of partitions, and Caccioppoli partitions

created on 06 Jan 2002
modified by leonardi on 17 Dec 2006


Published Paper

Inserted: 6 jan 2002
Last Updated: 17 dec 2006

Journal: Adv. Math. Sci. Appl.
Volume: 12
Number: 2
Pages: 725-753
Year: 2002


We introduce a general framework where countable partitions of a measure space $(X,\mathcal M,\mu)$ become elements of a metric space defined by means of a suitable distance function. After a detailed study of their metric properties, we consider partitions of $\mathbf R^n$ with locally finite interface area (Caccioppoli partitions). We present some meaningful results (in particular, P-decomposition and regularity) which can form a theoretical basis for the application to variational problems.