Calculus of Variations and Geometric Measure Theory

G. P. Leonardi

Infiltrations in immiscible fluids systems

created on 18 Sep 2001


Published Paper

Inserted: 18 sep 2001

Journal: Proceedings of the Royal Society of Edinburgh
Number: 131A
Pages: 425-436
Year: 2001


In this paper we prove a certain regularity property of configurations of immiscible fluids, filling a bounded container $\Omega$ and locally minimizing the sum over $i<j$ of $c_{ij} \
$, where $S_{ij}$ represents the interface between fluid $i$ and fluid $j$, $\
\cdot \
$ stands for area or more general area-type functional, and $c_{ij}$ is a positive coefficient. More precisely, we show that, under strict triangularity of the $c_{ij}$'s, no infiltrations of other fluids are allowed between two main ones. A remarkable consequence of this fact is the almost-everywhere regularity of the interfaces. Our analysis is performed in general dimension $n> 1$ and with volume constraints on fluids.

Keywords: Sets of finite perimeter, Immiscible fluids