Calculus of Variations and Geometric Measure Theory
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L. Granieri

Optimal Transport and Minimizing Measures

created by granieri on 12 Oct 2010
modified on 08 Mar 2012



Inserted: 12 oct 2010
Last Updated: 8 mar 2012

Journal: LAP Lambert Academic Press
Year: 2010

monograph LAP Editor


Mass transportation problems, also known as Monge-Kantorovich problems, have been intensively studied in particular with respect to numerous and important applications and connections with other fields such as PDE, material sciences, probability and economics. One of these connections is concerned with Mather's theory of minimal measures in Lagrangian dynamic. The main aim of this monograph is to present in a self-contained way some aspects of these connections and some related open problems as well. In particular, the main results presented are based on the notion of currents in Geometric Measure Theory. This monograph could be also considered as an introduction to the Monge-Kantorovich Theory by emphasizing the role of Geometric Measure Theory and some connections with Lagrangian dynamic.

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