Given a metric space $X$, we consider a class of action functionals, generalizing those considered in \cite{BBS} and \cite{AS}, which measure the cost of joining two given points $x_0$ and $x_1$, by means of an absolutely continuous curve. In the case $X$ is given by a space of probability measures, we can think of these action functionals as giving the cost of some congested/concentrated mass transfer problem. We focus on the possibility to split the mass in its {\it moving part} and its part that (in some sense) has already reached its final destination: we consider new action functionals, taking into account only the contribution of the moving part.
Curves of minimal action over metric spaces
BRASCO, Lorenzo
2010
Abstract
Given a metric space $X$, we consider a class of action functionals, generalizing those considered in \cite{BBS} and \cite{AS}, which measure the cost of joining two given points $x_0$ and $x_1$, by means of an absolutely continuous curve. In the case $X$ is given by a space of probability measures, we can think of these action functionals as giving the cost of some congested/concentrated mass transfer problem. We focus on the possibility to split the mass in its {\it moving part} and its part that (in some sense) has already reached its final destination: we consider new action functionals, taking into account only the contribution of the moving part.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
