Calculus of Variations and Geometric Measure Theory

L. Brasco

Curves of minimal action over metric spaces

created by brasco on 27 Mar 2009
modified on 08 Oct 2013


Accepted Paper

Inserted: 27 mar 2009
Last Updated: 8 oct 2013

Journal: Ann. Mat. Pura Appl.
Year: 2010


Given a metric space $X$, we consider a class of action functionals, generalizing those considered in Brancolini-Buttazzo-Santambrogio (J. Eur. Math. Soc. 8 (2006)) and Ambrosio-Santambrogio (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei -- Mat. Appl. 18 (2007)), 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 congestedconcentrated 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.

Keywords: Analysis in metric spaces, Minimizing curves, Branching transport